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Pulmonary hypertension (PH) is a debilitating disease that alters the structure and function of both the proximal and distal pulmonary vasculature. This alters pressure-flow relationships in the pulmonary arterial and venous trees, though there is a critical knowledge gap in the relationships between proximal and distal hemodynamics in disease. Multiscale computational models enable simulations in both the proximal and distal vasculature. However, model inputs and measured data are inherently uncertain, requiring a full analysis of the sensitivity and uncertainty of the model. Thus, this study quantifies model sensitivity and output uncertainty in a spatially multiscale, pulse-wave propagation model of pulmonary hemodynamics. The model includes fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. We quantify uncertainty in blood pressure, blood flow rate, wave intensity, wall shear stress, and cyclic stretch. The latter two are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal arterial and venous circulations.

The remarkable signal-detection capabilities of the auditory and vestibular systems have been studied for decades. Much of the conceptual framework that arose from this research has suggested that these sensory systems rest on the verge of instability, near a Hopf bifurcation, in order to explain the detection specifications. However, this paradigm contains several unresolved issues. Critical systems are not robust to stochastic fluctuations or imprecise tuning of the system parameters. Further, a system poised at criticality exhibits a phenomenon known in dynamical systems theory as critical slowing down, where the response time diverges as the system approaches the critical point. An alternative description of these sensory systems is based on the notion of chaotic dynamics, where the instabilities inherent to the dynamics produce high temporal acuity and sensitivity to weak signals, even in the presence of noise. This alternative description resolves the issues that arise in the criticality picture. We review the conceptual framework and experimental evidence that supports the use of chaos for signal detection by these systems, and propose future validation experiments.

The phenomenon of random wind speed fluctuations is an inherent characteristic of natural airflow, and it can significantly impact the power output of galloping-based piezoelectric energy harvesters (GPEHs). In this research, a stochastic model is developed to analyze the system performance considering the random variations in both the wind speed and the aerodynamic parameters derived from quasi-steady theory. Monte Carlo simulations are employed to evaluate the system performance under different degrees of randomness in the wind speed and the aerodynamic coefficients, accounting for quasi-steady theory assumptions. The findings of this study reveal that random variations in the galloping force coefficients exert a more pronounced influence on the electrical power output compared to wind speed. Moreover, the non-linear galloping force coefficient has a more significant influence on power output compared to the linear coefficient. [ABSTRACT FROM AUTHOR]

The focus of this paper is to examine the motion of a novel double pendulum (DP) system with two degrees of freedom (DOF). This system operates under specific constraints to follow a Lissajous curve, with its pivot point moving along this path in a plane. The nonlinear differential equations governing this system are derived using Lagrange's equations. Their analytical solutions (AS) are subsequently calculated using the multiple-scales method (MSM), which provides higher-order approximations. These solutions are considered new, as the traditional MSM has been applied to this novel system for the first time. Additionally, the accuracy of these solutions is validated through numerical results obtained using the fourth-order Runge–Kutta method. The solvability conditions and characteristic exponents are determined based on resonance cases. The Routh–Hurwitz criteria (RHC) are employed to assess the stability of the fixed points corresponding to the steady-state solutions. They are also used to demonstrate the frequency response curves. The nonlinear stability analysis is performed by examining the stability and instability ranges. Resonance curves and time history plots are presented to analyze the behavior of the system for specific parameter values. The investigation delves into a comprehensive analysis of bifurcation diagrams (BDs) and Lyapunov exponent spectra (LEs), aiming to uncover the various types of motion present within the system. Systematic examination of these charts reveals critical insights into transitions between stable, quasi-stable, and chaotic dynamical behaviors. This work has practical applications in various fields, such as robotics, pump compressors, rotor dynamics, and transportation devices. It can be used to study the vibrational motion of these systems. [ABSTRACT FROM AUTHOR]

This paper integrates event-triggered mechanisms and fixed-time control to address the cluster consensus problem of second-order nonlinear multi-agent systems (MASs) under the undirected communication topology. Firstly, a fractional-order-based nonlinear algorithm is proposed to obtain cluster consensus for second order MASs within a bounded settling time for any initial conditions. Secondly, to further save communication resources, double dynamic event-triggered mechanisms (DETMs), considering the dynamic parameters in the triggering conditions, are introduced, which control the communication among agents and the update of controllers asynchronously. In addition, Zeno behaviour is excluded by calculating the positive lower bound of the inter-event intervals. Finally, a simulation of Chua's circuit is given to verify the effectiveness and superiority of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a base excited, spring coupled double cantilever beam with attached tip mass based piezoelectric energy harvester. The dimensions of the beams are so chosen that the system experiences 1:1 internal resonance. The governing coupled electro-mechanical equations of motion of the system are obtained by using the Lagrange principle which is reduced to the temporal form by using generalized Galerkin's method. The governing temporal equations of motion are in the form of that of a parametrically excited coupled system with geometric and inertial nonlinearities. These nonlinear equations are solved using the method of multiple scales and the results are compared with those solved by numerical method (4th order Runge Kutta method) for principal parametric resonance conditions. Parametric studies are conducted by varying the tip masses of the beams, coupled spring stiffness, load resistance, external excitation frequency and excitation amplitude. Results show that by introducing spring coupling, the system operational frequency range increases significantly and also energy transfer process takes place due to the internal resonance. Significant enhancement of voltage and power are observed in the present work in comparison to the earlier studied equivalent single beam-based energy harvester. [ABSTRACT FROM AUTHOR]

For the systems modeled by a generalized reaction–diffusion equation with the higher‐order quintic nonlinearity, we explore the soliton dynamics via the F‐expansion method. By the novel F‐base function ansatz, we first derived the bright soliton and kink soliton solutions for the one‐dimensional case of the reaction–diffusion equation with quintic nonlinearity. Furthermore, we employed self‐similar techniques to analyze the higher‐dimensional dynamics of bright soliton and kink soliton solutions supported by the (2+1)‐dimensional reaction–diffusion equation system with quintic nonlinearity. Additionally, we conducted stability analysis of derived soliton solutions. Our theoretical results demonstrate that under certain parametric setting, the reaction–diffusion equation model with higher‐order nonlinearity supports bright soliton and kink soliton in higher‐dimensional as well as lower dimensional setting, which provides guidance for observing and investigating soliton behavior in systems modeled by the reaction–diffusion equation with higher‐order quintic nonlinearity. [ABSTRACT FROM AUTHOR]

El Niño–Southern Oscillation (ENSO) exhibits a considerable asymmetry in sea surface temperature anomalies (SSTa), as El Niño events tend to be stronger and centered further east than La Niña events. Here, we analyze ENSO asymmetry in observations and preindustrial control integrations of 32 models participating in phase 6 of the Coupled Model Intercomparison Project (CMIP6). Observations indicate a significant link between strong eastern Pacific (EP) El Niño events and the ENSO amplitude and asymmetry. The large CMIP6 database confirms this strong link. Most CMIP6 models suffer from an equatorial Pacific cold SST bias. This cold tongue bias hinders the southward migration of the ITCZ toward the equator over the eastern equatorial Pacific, which is characteristic of strong EP El Niño events in observations. Therefore, many models underestimate the eastern equatorial Pacific rainfall anomalies and simulate a wind stress feedback over the western Pacific that is too weak and too far west. As a result, the cold tongue bias exerts a strong control on the climate models' ability to generate strong EP El Niño events and therefore on the ENSO overall amplitude and asymmetry. We discuss the relevance of these results in view of a potential increase of strong EP El Niño events under global warming. Significance Statement: El Niño and La Niña are asymmetric, as El Niño events tend to be stronger and further east than La Niña events. Due to an equatorial Pacific cold tongue bias with too cold SSTs, the simulation of ENSO asymmetry is degraded in many climate models participating in CMIP6. Here, we show how the cold tongue bias influences ENSO asymmetry. The cold bias hampers the simulation of strong eastern Pacific El Niños by making it more difficult for SST to exceed the threshold for deep atmospheric convection over the eastern equatorial Pacific. Recent research indicates that climate models with a realistic ENSO asymmetry agree on the projected ENSO under global warming. The results of this study suggest that reducing the cold tongue bias has the potential to enhancing the reliability of future ENSO projections. [ABSTRACT FROM AUTHOR]

Recent simulations performed with the Community Earth System Model (CESM) have suggested a crucial role of sea ice processes in Atlantic meridional overturning circulation (AMOC) hysteresis behavior under varying surface freshwater forcing. Here, we further investigate this issue using additional CESM simulations and a novel conceptual ocean–sea ice box model. The CESM simulations suggest that the presence of sea ice gives rise to the existence of statistical equilibria with a weak AMOC strength. This is confirmed in the conceptual model, which captures similar AMOC hysteresis behavior as in the CESM simulation and where steady states are computed versus freshwater forcing parameters. In the conceptual model, transition probabilities between the different equilibrium states are determined using rare event techniques. The transition probabilities from a strong AMOC state to a weak AMOC state increase when considering sea ice insulation effects and indicate that sea ice promotes these transitions. On the other hand, sea ice insulation effects strongly reduce the probabilities of the reverse transition from a weak AMOC state to a strong AMOC state and this implies that sea ice also limits AMOC recovery. The results here indicate that sea ice effects play a dominant role in AMOC hysteresis width and influence transition probabilities between the different equilibrium states. Significance Statement: We develop a novel conceptual ocean–sea ice box model to explain AMOC hysteresis behavior recently found in a modern complex climate model (the Community Earth System Model) and determine how sea ice insulation effects influence the hysteresis width and the probability of AMOC transitions. [ABSTRACT FROM AUTHOR]

In this study, we analyze a symmetrical anharmonic oscillator that differs from a basic harmonic oscillator by including additional terms in the potential energy function. This oscillator's nonlinear characteristics are important in many physics fields, allowing for modeling of complex systems. We begin by creating the Lagrangian and obtaining the equation of motion through the Euler–Lagrange equation. Both the multi-step differential transforms method (Ms-DTM) and the Runge–Kutta 4th-order (RK4) method are employed to solve this equation, providing both analytical and numerical solutions. By examining these solutions, we confirm our findings and enhance our comprehension of the oscillator's behavior, which can be applied to more intricate nonlinear systems. [ABSTRACT FROM AUTHOR]

The 3D modeling analysis for the rotary motion of an asymmetric rigid body (RB) that gains a charge is presented. Under the effect of a gyrostatic moment (GM), an electromagnetic force field (EFF), time-varying body-fixed torques (TVBFTs), and constant axial torque (CAT), Euler's equation of motion (EOM) is derived to describe the body's EOM. The process is to derive the analytic solutions for the general attitude motion of the RB that is nearly symmetrical; therefore, a novel analytical solution for the angular velocities of the body has been approached. These new solutions are obtained by considering torques that vary over time and expressing them as integrals. Additionally, a novel closed-form evaluation mechanism for these integrals is offered. Specifically, the case of a constant torque around the spin axis and transverse torques represented by polynomial functions of time is explored. When dealing with an axisymmetric RB subject to a CAT, the solutions obtained from Euler's EOM are exact. However, it is important to note that novel analytic solutions for the Eulerian angles are approximations, as they rely on the assumption of small angles. Nonetheless, these approximations have broad applicability to a wide range of practical problems. The method's precision is demonstrated through the graphical simulation of the proposed solutions. Additionally, a computer program is utilized to create diagrams and phase plane curves, highlighting the contribution of various body parameters to the motion. These plots depict the contributions of various values regarding GM, charge, and CAT. Motion stability is also examined through phase diagrams. In addition to presenting novel solutions and outcomes for the problem, this study plays a vital role in multiple scientific and engineering fields as it has the potential to optimize mechanical systems, explain celestial motion, and improve spacecraft performance. [ABSTRACT FROM AUTHOR]

This work studies the nonlinear movement of a two degrees-of-freedom (DOF) spring pendulum that is dampened and affected by a harmonic force externally. It is presumed that the spring's pivot point travels along an elliptic route. Lagrange's equations are utilized to generate the regulating system of motion. The multiple-scales approach (MSA) is used to gain the system's analytic solutions up to the third-order approximation. Therefore, all resonance cases that have emerged are categorized, wherein two of them are scrutinized at once. As a result of the removal of secular terms, the solvability constraints are attained and then the steady-state solutions are investigated. The examined motion's temporal evolution, the resonance response curves, and the solutions at the steady-state are all depicted graphically. In compliance with the Routh–Hurwitz criteria (RHC), all possible fixed points (FPs) for the steady and unsteady cases are found and displayed. The stability zones are examined and analyzed to estimate the effect of various factors on the system's behavior. This model has gained prominence recently due to its industrial uses in seismic isolation systems for buildings and structures. However, in seismic engineering, a 2DOF vibrating pendulum system can be used as part of a seismic isolation system designed to protect buildings and infrastructure from earthquake-induced vibrations. The pendulum mechanism helps to absorb and dissipate seismic energy, reducing the amount of force transmitted to the structure. During an earthquake, the ground motion acts as an external harmonic force on the building. The distribution of mass and the structural layout can cause rotational moments that act on the building. The pendulum system can be tuned to counteract these moments, helping to stabilize the structure. The pendulum system allows for both horizontal and vertical displacement, providing two degrees of freedom. This capability is essential for accommodating the complex, multi-directional nature of seismic waves. [ABSTRACT FROM AUTHOR]

This study focuses on determining the required minimum-time (MT) for the spatial motion of a free rigid body (RB) experiencing gyrostatic moments (GMs) and viscous friction. The study assumes that the body's center of mass coincides with the original point of two Cartesian systems of coordinates. An optimal control law for slow motion is established, and the corresponding time and phase pathways are analyzed. The innovative results are presented for two new cases through various graphs highlighting the positive effects of the GMs. A comparison is achieved between the obtained results and previous outcomes that did not consider gyrostatic moments, showing remarkable consistency with slight deviations that are discussed. The practical applications of this study, which limits itself to using gyroscopic theory to maintain the stability and balance of vehicles in which gyroscopes are used, as well as figuring out the trajectory of aircraft and marine vehicles, are what make it noteworthy. [ABSTRACT FROM AUTHOR]

Curved shell structures with variable cross-sections are extensively applied in options for deep space exploration and on-orbit operation, due to their better mechanical properties compared to traditional materials. However, these structures also pose challenging dynamic modeling issues due to their nonlinear geometry and high flexibility. In this paper, the improved absolute nodal coordinate formulation (S-A-ANCF) is proposed for analyzing the dynamic behaviors of curved shells with variable cross-sections. Firstly, the neutrosphere of the curved shell is corrected to accurately describe the displacement field. Secondly, reduction factors for meshing are proposed by considering the aspect ratio criterion and shear performance criterion, which are then combined with the Enhanced Assumed Strain (EAS) method to establish the S-A-ANCF model. Finally, the correctness of the proposed method is verified through numerical analysis, and the optimized criterion for the modeling process is analyzed. According to the numerical analysis, the proposed method effectively improves modeling accuracy and efficiency. The coupling relationships between geometry, materials, boundary conditions, and stress are illustrated. The research outcomes of this paper can provide theoretical guidance for spacecraft systems with curved shells, which are of great significance and urgently need to be studied. [ABSTRACT FROM AUTHOR]

The paper utilizes a novel approach for the dynamic design of automotive turbocharger rotors by employing nonlinear dynamics of time periodic systems, emphasizing the influence of bearing design variables to prevent sub-synchronous components in system's response. The investigation focuses on the response of an unbalanced turbocharger rotor on floating ring bearings using a collocation-type method which has been developed for the needs of the work, being then integrated with pseudo arc length continuation for the calculation of unstable solution branches of the system, in several design sets, and with poor initial values. The analytical model includes a rigid rotor model and short bearing approximations for the two floating ring bearings, which introduce strong nonlinear forces in series (inner film and outer film at each bearing). Floquet theory is employed to analyse the non-autonomous dynamic system, and stability characteristics of the response limit cycles are assessed through Floquet multipliers, whose magnitude serves as a stability index in the algorithm. A genetic algorithm based multi-objective optimization is combined to the robust collocation-type method to achieve reduced values for Floquet multipliers, ensuring that response limit cycles maintain stability and periodicity, thereby preventing the occurrence of bifurcations which normally lead to sub-synchronous response components. Twelve design variables are computed to satisfy low rotor eccentricity and power loss. Acceptable design sets are verified for efficacy by assessing system response through time integration, akin to a virtual experiment. This approach significantly reduces computational time and resource requirements compared to traditional Design of Experiment (DoE) procedures and is not constrained by complex models of the rotor, bearings, or other components. A feature of the method is that it offers an insight on the stability and its quality, rather than simply assessing a threshold speed of instability. [ABSTRACT FROM AUTHOR]

To accurately investigate the nonlinear dynamic characteristics of a flyback converter, a fractional-order state-space averaged model of a voltage mode controlled flyback converter in continuous conduction mode is established based on fractional calculus theory. And low-frequency bifurcation maps which use PI controller parameters and reference voltage as bifurcation parameters are obtained. The low-frequency oscillation phenomenon is analyzed and compared with that of an integral-order flyback converter. The results show that under certain operating conditions, the fractional-order flyback converter exhibits low-frequency oscillations as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the flyback converter. The stable zone of the fractional-order flyback converter is larger than that of the integral-order one. Therefore, the circuit is more difficult to enter a low-frequency oscillation state. The stability domain of low-frequency oscillations can be accurately predicted by using the small signal model of the fractional-order flyback converter. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified. [ABSTRACT FROM AUTHOR]

A local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones. [ABSTRACT FROM AUTHOR]

This study aims to solve the nonlinear Pochhammer–Chree (ℕℙℂ) equation to understand its physical implications and establish connections with other nonlinear evolution equations, particularly in plasma dynamics. By using the Khater II (핂hat. II) method for analytical solutions and validating these solutions numerically with the variational iteration method, this study offers a detailed understanding of the equation’s behavior. The results demonstrate the effectiveness of these methods in accurately modeling the system, highlighting the importance of combining analytical and numerical approaches for reliable solutions. This research significantly advances the field of nonlinear dynamics, especially in plasma physics, by employing multidisciplinary methods to tackle complex physical processes. Moreover, the ℕℙℂ equation is relevant in various physical contexts beyond plasma dynamics such as optical and quantum fields. In optics, it models the propagation of nonlinear waves in fiber optics, where similar nonlinear evolution equations describe wave interactions. In quantum field theory, the ℕℙℂ equation helps in understanding the behavior of quantum particles and fields under nonlinear effects, making it a versatile tool for studying complex phenomena across different domains of physics. [ABSTRACT FROM AUTHOR]

Qualitative changes can occur in the dynamics of nonlinear systems even for small parameter variations. Such changes are manifestations of bifurcation in dynamical systems. In the context of differential game theory, bifurcations offer insights into the underlying mechanisms driving strategic interactions and identify transitions between different types of behavior. Such critical transitions are tipping points that can dramatically change the outcomes of the game. This work explores the possibility of predicting such qualitative shifts, including supercritical Hopf bifurcations, before they occur using a data-driven forecasting technique. This concept is demonstrated for an attacker–defender game in a limited resource scenario and for an active cybersecurity defense game. The time histories of the system dynamics as it approaches a bifurcation allow one player to detect the existence of bifurcations. This capability provides that player insights into the dynamics of the game and potential defense mechanisms in resource-constrained scenarios. [ABSTRACT FROM AUTHOR]

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass–spring–damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Stride-to-stride fluctuations during walking reflect age-related changes in gait adaptability and are estimated with nonlinear measures that confine data collection to controlled settings. Smartphones, with their embedded accelerometers, may provide accessible gait analysis throughout the day. This study investigated age-related differences in linear and nonlinear gait measures estimated from a smartphone accelerometer (SPAcc) in an unconstrained, free-living environment. Thirteen young adults (YA) and 11 older adults (OA) walked within a shopping mall with a SPAcc placed in their front right pants pocket. The inter-stride interval, calculated as the time difference between ipsilateral heel contacts, was used for dependent measures calculations. One-way repeated-measures analysis of variance revealed significant (p < 0.05) age-related differences (mean: YA, OA) for stride-time standard deviation (0.04 s, 0.05 s) and coefficient of variation (3.47%, 4.16%), sample entropy (SaEn) scale 1 (1.70, 1.86) and scale 3 (2.12, 1.80), and statistical persistence decay (31 strides, 23 strides). The fractal scaling index was not different between groups (0.93, 0.95), but exceeded those typically found in controlled settings, suggesting an upregulation in adaptive behaviour likely to accommodate the increased challenge of free-living walking. These findings support the SPAcc as a viable telehealth instrument for remote monitoring of gait dynamics, with implications for unsupervised fall-risk assessment. [ABSTRACT FROM AUTHOR]

This paper evaluates the nonlinear dynamics of a melanoma cancer model through the iterative technique of finding compact invariant sets (LMCIS). The objective is to discover equilibrium points, ascertain their stability qualities, and determine the presence of compact invariant sets within the model. For instance, this approach is assessed in a model demonstrating the interplay between four cellular populations and administrating interleukin-12 (IL-12) immunotherapy. Nevertheless, the mechanism by which this anti-cancer therapy operates has yet to be completely defined. The approach is evaluated using severe treatment situations to provide evidence for the presence of equilibrium points inside the iteratively confined zone and to assess its effectiveness. The outcomes derived from using this approach were then compared with a conventional iteration of Newton's method. Newton's approach extends to the resolution of the system of equations inside the model, facilitating the identification of the equilibrium points with a small tolerance error. While the iterations of the localization algorithm were set close to the results obtained by this method. Finally, the simulation outcomes are shown via the utilization of MATLAB R2020b. The findings demonstrate the temporal progression of the model under the effect of immunotherapy and without it. [ABSTRACT FROM AUTHOR]

Numerical continuation tools are nowadays standard to analyse nonlinear dynamical systems by numerical means. These powerful methods are unfortunately not available in real experiments without having access to an accurate mathematical model. Implementing such a concept in real world experiments using control and data processing to track unstable states and their bifurcations, requires robust control techniques with large basins and good global properties. Here we propose design principles for control techniques for periodic states which lead to large basins and which are robust, without the need to have access to a detailed mathematical model. Our analytic considerations for the control design will be based on weakly nonlinear analysis of periodically driven oscillator systems. We then demonstrate by numerical means that in strong nonlinear regimes successful control with large basins of attraction can be achieved when only plain time series data are available. [ABSTRACT FROM AUTHOR]

This paper presents a compact method for selecting the suboptimal number of clusters in unsupervised clustering, which is comparable in complexity to the well-known elbow method, silhouette score and gap statistic, but has been upgraded for clustering with the dominant overlaps. It is primarily based on heuristics and combines human reasoning with the deterministic qualitative analysis of clustering as a mapping from Euclidean space to the unstructured space of cognitive decision making and labeling. Epistemic stability as a notation involves a methodological approach that takes into account the available knowledge in the observed data set and avoids biases and effects on the objectivity of clustering. The stability discussion is also integrated into the assigned and naturally quantitative analysis of the dataset, not to regulate the clustering, but to learn from the pattern of instability. The method is applied to the specific task of classifying medical images from pre-selected image sets based on the associated metadata to determine the homogeneity of the analyzed clusters. However, it is also applicable to any other example of datasets that exhibit statistically multivariate problems with dominant overlaps. In the mathematical discussion of the method presented, the constrained conditions for datasets are established by definitions and assumptions, followed by the central mathematical propositions of the method of epistemic stability. [ABSTRACT FROM AUTHOR]

Since the inception of nonlinear vibration theory, the majority of research has been focused on the elastic beams connected to a variety of nonlinear factors. Notwithstanding this, coupling beam systems with nonlinear coupling elements have been the subject of few investigations. In light of the fact that numerous coupling beam systems are typically connected via multiple couplers, this study develops a vibration model for two beams coupled by multiple nonlinear elements exhibiting cubic stiffness. The Lagrange method is utilized to compute the magnitude responses of the beam system. Once the accuracy and consistency of the magnitude responses associated with the beam system have been confirmed, a thorough investigation is conducted into the impact of nonlinear elements on the magnitude responses of two beams joined by multiple nonlinear elements exhibiting cubic stiffness. Nonlinear responses, such as peak jumping, intricate responses, and shifting resonance regions, are determined to be the result of nonlinear elements, according to simulation results. Modulating the parameters of nonlinear elements in a rational manner facilitates the regulation of vibrations across multiple resonance regions of the beam system. Parameter changes of nonlinear elements have a substantial impact on both the vibration states and peak values of magnitude responses for single-frequency vibration excitation in resonance regions. The incorporation of nonlinear components into the coupling beam system enables the regulation of both frequency and single-frequency responses. In the case of low damping, nonlinear vibration control for a system consisting of two beams through the use of multiple nonlinear elements with cubic stiffness is more effective. [ABSTRACT FROM AUTHOR]

This paper delves into the exploration of directional recursion operators within the realm of regular space curves modeled by Heisenberg systems. The central objective is to introduce a myriad of recursive flows, encompassing ferromagnetic and antiferromagnetic solutions, alongside a family of general normalization operators in the normal and binormal directions. The study employs the extended compatible and inextensible flow model of curves to examine the evolution models, providing a comprehensive understanding of their dynamics. A significant aspect of the investigation involves elucidating the evolution model in terms of anholonomy shapes and their density. The directional recursive operator, a focus of this study, demonstrates distinct results compared to traditional approaches. The reliability and applicability of the obtained results extend to the examination of various linear and nonlinear continuous dynamical systems. [ABSTRACT FROM AUTHOR]

In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton's principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam's multidimensional system. [ABSTRACT FROM AUTHOR]

The signature of cognitive involvement in gait control has rarely been studied using both kinematic and neuromuscular features. The present study aimed to address this gap. Twenty-four healthy young adults walked on an instrumented treadmill in a virtual environment under two optic flow conditions: normal (NOF) and perturbed (POF, continuous mediolateral pseudorandom oscillations). Each condition was performed under single-task and dual-task conditions of increasing difficulty (1-, 2-, 3-back). Subjective mental workload (raw NASA-TLX), cognitive performance (mean reaction time and d-prime), kinematic (steadiness, variability, and complexity in the mediolateral and anteroposterior directions), and neuromuscular (duration and variability of motor primitives) control of gait were assessed. The cognitive performance and the number and composition of motor modules were unaffected by simultaneous walking, regardless of the optic flow condition. Kinematic and neuromuscular variability was greater under POF compared with NOF conditions. Young adults sought to counteract POF by rapidly correcting task-relevant gait fluctuations. The depletion of cognitive resources through dual-tasking led to reduced kinematic and neuromuscular variability and this occurred to the same extent regardless of simultaneous working memory (WM) load. Increasing WM load led to a prioritization of gait control in the mediolateral direction over the anteroposterior direction. The impact of POF on kinematic variability (step velocity) was reduced when a cognitive task was performed simultaneously, but this phenomenon was not modulated by WM load. Collectively, these results shed important light on how young adults adjust the processes involved in goal-directed locomotion when exposed to varying levels of task and environmental constraints. NEW & NOTEWORTHY: The kinematic and neuromuscular signatures of cognitive involvement in gait control have rarely been studied jointly. We sought to address this issue using gait perturbation and dual-task paradigms. The protocol consisted of a fixed-speed treadmill walk to which visual and cognitive constraints were applied separately and together. The results revealed that young adults optimally regulated their gait to cope with these constraints by maintaining relatively stable muscle synergies and flexibly allocating attentional resources. [ABSTRACT FROM AUTHOR]

Connected automated vehicles (CAVs) have the potential to improve the efficiency of vehicular traffic. In this paper, we discuss how CAVs can positively impact the dynamic behavior of mixed traffic systems on highways through the lens of nonlinear dynamics theory. First, we show that human-driven traffic exhibits a bistability phenomenon, in which the same drivers can both drive smoothly or cause congestion, depending on perturbations like a braking of an individual driver. As such, bistability can lead to unexpected phantom traffic jams, which are undesired. By analyzing the corresponding nonlinear dynamical model, we explain the mechanism of bistability and identify which human driver parameters may cause it. Second, we study mixed traffic that includes both human drivers and CAVs, and we analyze how CAVs affect the nonlinear dynamic behavior. We show that a large-enough penetration of CAVs in the traffic flow can eliminate bistability, and we identify the controller parameters of CAVs that are able to do so. Ultimately, this helps to achieve stable and smooth mobility on highways. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This work was supported by the University of Michigan's Center for Connected and Automated Transportation [U.S. DOT Grant 69A3551747105]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0498. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface. [ABSTRACT FROM AUTHOR]

Extratropical storms, particularly explosive storms or "weather bombs" with exceptionally high deepening rates, present substantial risks and are susceptible to climate change. Individual storms may exhibit a complex and hardly detectable response to human-driven climate change because of the atmosphere's chaotic nature and variability at the regional level. It is thus essential to understand changes in specific storms for building local resilience and advancing our overall comprehension of storm trends. To address this challenge, this study compares analogs—storms with a similar backward track until making landfall—in two climates of three explosive storms impacting different European locations: Alex (October 2020), Eunice (January 2022), and Xynthia (February 2010). We use a large ensemble dataset of 105 members from the Community Earth System Model, version 1 (CESM1). These analogs are identified in two periods: the present-day climate (1991–2001) and a future climate scenario characterized by high anthropogenic greenhouse gas emissions [representative concentration pathway 8.5 (RCP8.5), 2091–2101]. We evaluate future changes in the frequency of occurrence of the storms and intensity, as well as in meteorological hazards and the underlying dynamics. For all storms, our analysis reveals an increase in precipitation and wind severity over land associated with the explosive analogs in the future climate. These findings underscore the potential consequences of explosive storms modified by climate change and their subsequent hazards in various regions of Europe, offering evidence that can be used to prepare and enhance adaptation processes. Significance Statement: This study investigates the impact of climate change on explosive storms, or weather bombs, and their potential consequences for European regions. We project future scenarios of three specific storms, Alex, Eunice, and Xynthia, using a state-of-the-art climate model. Our findings reveal an increase in precipitation and wind over land associated with these storms, emphasizing the heightened risks associated with climate change. The significance lies in understanding the local implications of explosive storms, aiding in the development of resilient strategies and adaptation measures. [ABSTRACT FROM AUTHOR]

The tire/road noise is one of the major problems facing the tire industry due to the nuisance felt by the vehicle's driver and passengers. Moreover, it is expected in the coming years that this sound nuisance will be one of the main sources of vehicle noise due to the transition from combustion engine driven vehicles to electric vehicles. Tire manufacturers have therefore refined the design of their tire structures to find technological solutions to reduce traffic noise. Tire/road noise is also generated by various mechanisms which depend on different parameters such as the properties of the tire, road texture and driving conditions. This noise is partly caused by the acoustic radiation induced by the tire vibrations due to contacts with the road. The simulation and analysis of the tire's vibrations remains a challenge for the tire industry. Indeed, the simulation of the full dynamic response of a rolling patterned tire requires not only taking onto account various nonlinearities but also the multi-scale nature of the generated dynamic response. Contrary to a straightforward strategy that consists in using a time integrator to predict the multi-scale dynamic response, the strategy proposed in this study is based on a two-step approach to separate the dynamics occurring at different scales. The mathematical formulation of the proposed method is detailed as are the different modeling choices to simulate tire rolling under imposed load. The sensitivity of the tire's vibrations response is analyzed under different rolling conditions and with respect to certain key tire tread pattern parameters. • An adapted two-step approach to simulate nonlinear vibrations by separating the dynamics occurring at different scales. • Mathematical formulation of the proposed method with different modeling choices to simulate tire rolling under imposed loads. • Application to patterned tires rolling on a smooth surface. • Examples of the tire's vibrations response under different rolling conditions and key tire tread pattern parameters. [ABSTRACT FROM AUTHOR]

This is a comprehensive overview on our research work to link interdisciplinary modeling and simulation techniques to improve the predictability and reliability simulations (PARs) of compressible turbulence with shock waves for general audiences who are not familiar with our nonlinear approach. This focused nonlinear approach is to integrate our "nonlinear dynamical approach" with our "newly developed high order entropy-conserving, momentum-conserving and kinetic energy-preserving methods" in the quantification of numerical uncertainty in highly nonlinear flow simulations. The central issue is that the solution space of discrete genuinely nonlinear systems is much larger than that of the corresponding genuinely nonlinear continuous systems, thus obtaining numerical solutions that might not be solutions of the continuous systems. Traditional uncertainty quantification (UQ) approaches in numerical simulations commonly employ linearized analysis that might not provide the true behavior of genuinely nonlinear physical fluid flows. Due to the rapid development of high-performance computing, the last two decades have been an era when computation is ahead of analysis and when very large-scale practical computations are increasingly used in poorly understood multiscale data-limited complex nonlinear physical problems and non-traditional fields. This is compounded by the fact that the numerical schemes used in production computational fluid dynamics (CFD) computer codes often do not take into consideration the genuinely nonlinear behavior of numerical methods for more realistic modeling and simulations. Often, the numerical methods used might have been developed for weakly nonlinear flow or different flow types other than the flow being investigated. In addition, some of these methods are not discretely physics-preserving (structure-preserving); this includes but is not limited to entropy-conserving, momentum-conserving and kinetic energy-preserving methods. Employing theories of nonlinear dynamics to guide the construction of more appropriate, stable and accurate numerical methods could help, e.g., (a) delineate solutions of the discretized counterparts but not solutions of the governing equations; (b) prevent numerical chaos or numerical "turbulence" leading to FALSE predication of transition to turbulence; (c) provide more reliable numerical simulations of nonlinear fluid dynamical systems, especially by direct numerical simulations (DNS), large eddy simulations (LES) and implicit large eddy simulations (ILES) simulations; and (d) prevent incorrect computed shock speeds for problems containing stiff nonlinear source terms, if present. For computation intensive turbulent flows, the desirable methods should also be efficient and exhibit scalable parallelism for current high-performance computing. Selected numerical examples to illustrate the genuinely nonlinear behavior of numerical methods and our integrated approach to improve PARs are included. [ABSTRACT FROM AUTHOR]

Ferroelectric field-effect transistors (FeFETs) with silicon channels and hafnia-zirconia ferroelectric films have been employed as silicon-friendly physical reservoir in reservoir computing application by leveraging the rich dynamics of polarization-polarization and polarization-charge interactions. FeFET reservoir computing exhibits promising computing performance with low error rate when predicting time-series generated from a nonlinear function and when classifying spoken digits for speech recognition. We investigate several approaches to improve the computing performance of FeFET reservoir computing including the optimization of input and readout schemes, the introduction of antiferroelectric-like materials with more complicated polarization dynamics, and the re-training to compensate the device degradation under electrical stress. [ABSTRACT FROM AUTHOR]

Shellfish cultivation is a sustainable method of providing human food and can help remove large amounts of CO2 from the atmosphere. Over the last two decades, longline-based structures have dominated farming systems. So far, the innovative technologies for open-ocean shellfish farming remain stagnant and need to be developed. As such, this paper preliminarily studies the operation and survivability abilities of an innovative shellfish farm under extreme wave conditions. To that end, an efficient numerical scheme with a robust implicit finite element method is established. First, the numerical modeling of a single module of the shellfish farm is conducted and the numerical results are verified against physical model tests. Then, the numerical modeling is implemented in a full-scale shellfish farm containing nine floating rafts with suspended lantern nets in a 3×3 configuration exposed to extreme wave conditions. Different angles of wave attack and shellfish rafts with and without lantern nets are fully considered, allowing an assessment of the operation and survivability abilities of the shellfish farm under extreme wave conditions in various situations. The results highlight that the angle of wave attack significantly affected the energy absorption of the mooring system. Moreover, non-linear instability such as subharmonics, which existed in the motion dynamics, can be manipulated to avoid resonant motions. This study provides insights into the evaluation of the safety design of a shellfish farm at both operational and survivability levels. The numerical method can also model other advanced offshore marine structures with multi-modules, such as floating bridges, airports, and even floating energy islands. [ABSTRACT FROM AUTHOR]

To achieve self-powered sensing when complex dynamics exist in fluid-conveying pipes, a novel piezoelectric energy harvesting configuration of cantilevered fluid-conveying pipes with an integrated stopper is proposed to investigate nonlinear dynamics, and elucidate the dynamic mechanism to enhance the energy harvesting performance. The nonlinear governing equation of this configuration was established by applying Hamilton's principle, and a set of ordinary differential equations was obtained using the Galerkin method. Considering the influence of a piezoelectric layer, the mode shapes with various orders of this configuration were determined by adopting the differential quadrature method. The harmonic balance method combined with the pseudo-arc length extension method was used to track the frequency responses, and the effectiveness of these responses was confirmed by comparing the analytical solutions to the numerical solutions obtained by the Runge–Kutta method. The global bifurcation diagrams, along with the phase trajectories, power spectra, and Poincaré maps, are presented to predict complex nonlinear dynamic behaviors, such as the coexistence of the system's periodic motion and chaotic motion. The results reveal that the impact force nonlinearity caused by the stopper can effectively improve the energy harvesting efficiency and make the dynamic behavior exhibit softening or hardening characteristics. Parametric investigations were conducted for the flow velocity, resistance, stiffness, and stopper position. The numerical examples reveal that the proposed system plays an important role in vibration suppression and energy harvesting. [ABSTRACT FROM AUTHOR]

This work presents a hybrid multidirectional mechanical energy harvester to enhance the performance of a cantilever-based harvester when subjected to multidirectional excitations. The multidirectional capabilities are achieved by employing a pendulum structure. Hybrid transduction is provided by combining a piezoelectric element and an electromagnetic transducer. A reduced-order model is presented based on the electromechanical Lagrangian formulation, and numerical analyses are performed to characterize the system behavior. A comparison based on energy harvesting performance is established among the novel multidirectional hybrid energy harvester (MHEH), the classical piezoelectric harvester (CPEH), and a multidirectional piezoelectric harvester (MPEH). Results show that the addition of the pendulum alone indeed provides multidirectional capabilities, but the overall performance can be reduced in some scenarios since it works as an energy absorber. This limitation is overcome by the hybridization strategy of the MHEH, by incorporating an electromagnetic transducer into the pendulum support. Overall, a significant improvement is achieved in all scenarios by utilizing the hybrid system. [ABSTRACT FROM AUTHOR]

The ultimate isolation offered by levitation provides new opportunities for studying fundamental science and realizing ultra-sensitive floating sensors. Among different levitation schemes, diamagnetic levitation is attractive because it allows stable levitation at room temperature without a continuous power supply. While the dynamics of diamagnetically levitating objects in the linear regime are well studied, their nonlinear dynamics have received little attention. Here, we experimentally and theoretically study the nonlinear dynamic response of graphite resonators that levitate in permanent magnetic traps. By large amplitude actuation, we drive the resonators into nonlinear regime and measure their motion using laser Doppler interferometry. Unlike other magnetic levitation systems, here we observe a resonance frequency reduction with amplitude in a diamagnetic levitation system that we attribute to the softening effect of the magnetic force. We then analyze the asymmetric magnetic potential and construct a model that captures the experimental nonlinear dynamic behavior over a wide range of excitation forces. We also investigate the linearity of the damping forces on the levitating resonator, and show that although eddy current damping remains linear over a large range, gas damping opens a route for tuning nonlinear damping forces via the squeeze-film effect. [ABSTRACT FROM AUTHOR]

Mechanical energy harvesting has increasing scientific and technological interests due to novel energetic challenges. A critical issue in classical cantilever-based mechanical energy harvesting systems is the lack of multidirectional energy conversion capabilities and, due to that, deviations from the excitation source can drastically reduce their performance. This limitation has led to the development of energy harvesters with attached pendula, serving as a direction coupling mechanism. Nevertheless, the pendulum structure itself can act as an energy absorber, drastically reducing the harvester performance in certain scenarios. In order to overcome this issue, a hybrid multidirectional pendulum-based energy harvester has been introduced by the authors. The hybrid transduction integrates a piezoelectric element to capture energy from the principal direction and an electromagnetic transducer to harness rotational energy from the pendulum. This paper presents an in-depth analysis of the hybrid multidirectional pendulum-based energy harvester using a nonlinear dynamics perspective to evaluate the energy harvesting performance. A reduced-order model is proposed to represent the essential characteristics of such systems. A parametric analysis using a nonlinear dynamics perspective is carried out to map the system dynamics and performance. The emergence of complex and rich dynamics is observed, including chaos and hyperchaos. Results reveal the most and least effective combinations of structural parameters in terms of energy conversion. Additionally, the dynamical responses and patterns associated with high performance are identified. These responses are often characterized by a blend of irregular complex behaviors, coupled with a mix of oscillatory and rotational patterns of motion, resulting in wider bandwidth systems. [ABSTRACT FROM AUTHOR]

Multi-sensory integration is a perceptual process through which the brain synthesizes a unified perception by integrating inputs from multiple sensory modalities. A key issue is understanding how the brain performs multi-sensory integrations using a common neural basis in the cortex. A cortical model based on reservoir computing has been proposed to elucidate the role of recurrent connectivity among cortical neurons in this process. Reservoir computing is well-suited for time series processing, such as speech recognition. This inquiry focuses on extending a reservoir computing-based cortical model to encompass multi-sensory integration within the cortex. This research introduces a dynamical model of multi-sensory speech recognition, leveraging predictive coding combined with reservoir computing. Predictive coding offers a framework for the hierarchical structure of the cortex. The model integrates reliability weighting, derived from the computational theory of multi-sensory integration, to adapt to multi-sensory time series processing. The model addresses a multi-sensory speech recognition task, necessitating the management of complex time series. We observed that the reservoir effectively recognizes speech by extracting time-contextual information and weighting sensory inputs according to sensory noise. These findings indicate that the dynamic properties of recurrent networks are applicable to multi-sensory time series processing, positioning reservoir computing as a suitable model for multi-sensory integration. [ABSTRACT FROM AUTHOR]

This work studies the impact between spherical rigid bodies in the frame of nonsmooth contact dynamics considering friction effects. A new impact element formulation based on the classical instantaneous local Newton impact law is presented. The kinematics properties of the spheres are described by a rigid body formulation with translational and rotational degrees of freedom referred to an inertial frame. In addition, an extension of the nonsmooth generalized‐α$$ \alpha $$ time integration scheme applied to collisions with multiple impacts including Coulomb's friction law is given. Six numerical examples are presented to evaluate the robustness and the performance of the proposed methodology. [ABSTRACT FROM AUTHOR]

Harvesting energy from nonlinear systems has been at the centre of research in the energy harvesting community. Many such proposed systems are single nonlinear harvester. While these systems show an increase in bandwidth of harvesting frequency, overall, they are not effective enough in power generation. This article studies power harvesting and frequency bandwidth characteristics of an array of harvesters. Multiple harvesters are considered with linear and nonlinear coupling between the harvesters. The phenomena of internal resonance (IR) and stochastic resonance (SR) are reported. The IR in multiple coupled nonlinear harvesters is explored using multiple-scale analysis. A parametric study is conducted to demonstrate the effect of coupling strength, frequency mistuning, innate nonlinearity and other parameters. The parametric study helped establish effective ways to increase bandwidth. Moreover, a stochastically loaded linearly coupled bistable harvester array is numerically analysed to find the effect of coupling strength and array size on the phenomenon of SR and on the system's harvesting performance. Through these studies, the potential of multiple coupled nonlinear harvesters in enhanced energy harvesting is demonstrated under both harmonic and stochastic excitation. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the nonlinear dynamic response and vibration characteristics of a car’s hood door, focusing on its energy capacity under various excitation frequencies. The hood door is modeled using a functionally graded triply periodic minimal surface (FG-TPMS) material, which offers superior mechanical properties and lightweight design. The analysis is conducted using a higher-order shear deformation theory (HSDT), which accounts for shear deformations more accurately than classical theories. The incorporation of von Karman nonlinear terms captures the geometric nonlinearity due to large deformations, providing a realistic simulation of the hood door’s behavior under dynamic loads. To solve the complex equations of motion derived from the HSDT and von Karman terms, a fourth-order Runge–Kutta method is employed. This numerical method ensures accurate time integration and stability of the solution. The dynamic response is further analyzed to determine the energy absorption capacity of the hood door material, crucial for safety and durability in automotive applications. Validation of the numerical model is performed using previous published articles and a hybrid machine learning algorithm, which combines data-driven approaches with traditional physics-based models. This hybrid validation enhances the accuracy and reliability of the predicted responses, ensuring that the proposed model can be effectively used in the design and optimization of car components. The results demonstrate the potential of FG-TPMS materials in automotive applications, offering improved energy absorption and vibration control, which are essential for enhancing vehicle safety and performance. [ABSTRACT FROM AUTHOR]

• The BLNNAC scheme is presented for finite-time stability. • The proposed node selection strategy in BLNN can improve the approximation ability. • A BLNN-based NDO is designed to eliminate the adverse impact of disturbances. In this work, a novel broad learning neural network based adaptive control (BLNNAC) scheme is designed for a class of spacecraft proximity systems with external perturbations, unmodeled dynamics and symmetrical time-varying constraints. Firstly, for avoiding the unacceptable complexity caused by conventional Barrier Lyapunov function, the constrained output signals are transformed into unconstrained ones by several nonlinear functions. Secondly, by virtue of fast response and insensitivity to external disturbance, the integral sliding-mode control (ISMC) scheme is incorporated into the presented control scheme. Then, to suppress the adverse impact of the dynamic uncertainties, a novel broad learning neural network (BLNN) is established to ameliorate the approximation performance. Based on that BLNN scheme, a nonlinear disturbance observer (NDO) is designed to approach the time-varying disturbances. Furthermore, a fractional power function, as a particular term of control input, is designed to guarantee the fast convergence rate. It is shown that all the signals are bounded, and the transient-states of the output signals satisfy the constraint conditions constantly. Finally, simulation results illustrate the effectiveness and advantages of the presented scheme. [ABSTRACT FROM AUTHOR]

Membrane reactors for the production of hydrogen are interesting devices that allow for the decentralized production of pure hydrogen while reducing the energy cost of the traditional steam reforming process. The performance of these systems is strongly dependent on the permeability and selectivity of the membrane employed for the separation of the produced hydrogen. Several studies have shown that the actual rate of hydrogen permeation is lower than the one that would be expected based on studies of membrane permeability carried out with pure hydrogen. This difference has been attributed to the competitive adsorption of other species, specifically CO, on the membrane surface. Here we show that this phenomenon could also lead to steady state multiplicity and analyze the dynamics of membrane reactors in the presence of competitive adsorption by CO. Emphasis has been placed on the effect of temperature and gas composition on possible multistable behavior. The results have been interpreted in terms of a transition between kinetics- and permeation-controlled regimes, in which the behavior of the reactor is limited, respectively, by the rate of the chemical reactions or the rate of hydrogen permeation. [Display omitted] • Dynamics of membrane reactors in the presence of permeance inhibition were analyzed. • Effect of gas composition and temperature on multistable behavior was investigated. • Relationship between observed multistability and membrane inhibition was assessed. • Multistability due to competition between rate of H 2 production and permeation is observed. [ABSTRACT FROM AUTHOR]

Chua's circuit represents a paradigm for nonlinear dynamics and chaos in electronic circuits. In this paper, its discrete-time counterpart is considered showing the occurrence of nonlinear resonance when driven by an external sinusoidal input. Evidences of jump resonance are revealed from several regions of the parameter space. An approach based on quasi-analytic methods, numerical simulations and several experiments with digital microprocessors is presented, further confirming the richness of Chua's circuit dynamical behavior. The high selectivity of the jump resonance observed from the discrete-time Chua's circuit paves the way for the implementation of low-cost high-resolution frequency drift sensing devices. [ABSTRACT FROM AUTHOR]

The purpose of this study is to investigate the effect of task constraints on the neurobiological systems while maintaining postural control under various sensory feedback manipulations in individuals with and without Chronic Ankle Instability (CAI). Forty-two physically active individuals, with and without CAI, were enrolled in a case-control study conducted at a biomechanics research laboratory. All participants underwent the Sensory Organization Test (SOT), which assesses individuals' ability to integrate somatosensory, visual, and vestibular feedback to maintain postural control in double-, uninjured-, and injured-limb stances under six different conditions in which variations in the sway-referenced support surface (platform) and visual surroundings, with and without vision, are manipulated to affect somatosensory and visual feedback. Center-of-Pressure (COP) path length was computed from raw data collected during trials of each SOT condition. Sample Entropy (SampEN) values were extracted from the COP path length time series to examine neurobiological systems complexity, with lower SampEN values indicating more predictable and periodic (rigid) neurobiological systems, while higher SampEN values indicate more unpredictable and random systems. The results show that specific task constraints affect the neurobiological systems. Specifically, individuals with CAI demonstrated reduced complexity (decreased SampEN values) in the neurobiological systems during the uninjured-limb stance when all sensory feedback was intact and during both uninjured- and injured-limb stances when they were forced to rely on vestibular feedback. These results highlight the interplay between sensory feedback and task constraints in individuals with CAI and suggest potential adaptations in the neurobiological systems involved in postural control. [ABSTRACT FROM AUTHOR]

In this article, we propose a new perspective mathematical model of the beam with the distributed hysteresis properties. Hysteresis properties are formalized within two approaches: phenomenological (Bouc-Wen model) and design (Prandtl-Ishlinskii model). The equations for the beam vibrations are obtained using the well-known Hamilton approach. The dynamical response of the beam with distributed hysteresis is considered under various types of external load, such as impulse, periodic, and a seismic load. Numerical simulations show that the hysteresis beam is more "resistant" to external loads than the classical Euler-Bernoulli beam. Particularly, with the same types of the external load, the amplitude of oscillations of the hysteresis beam as well as its energy characteristics are lower than those of the classical one. These results may find some applications in the field of the design of earthquake-resistant constructions and buildings. [ABSTRACT FROM AUTHOR]

The multi-gear parallel drive system of TBM is susceptible to many nonlinear factors in the driving process, which seriously affects the dynamic performance of the system. This paper takes the six-gear parallel transmission system as the research object, introduces the influence of several nonlinear factors such as thermal deformation, establishes the dynamic model of the system, adopts the Runge-Kutta method to carry out simulation calculation, and studies the dynamic characteristics of the system by combining the bifurcation diagram and Lyapunov diagram. The results indicate that when the temperature is below 58.43 °C or above 70.4 °C, with a stiffness coefficient below 0.35 and a damping ratio above 0.069, it can suppress chaotic motion, reduce system vibration and noise. Furthermore, beyond 58.43 °C and 70.4 °C, variations in stiffness and damping ratios have a minimal impact on the system's motion characteristics, indicating that higher temperatures can enhance system stability. [ABSTRACT FROM AUTHOR]