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We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called correlation dimension (or Rényi entropy). We study the analogous quenched question, and show that the asymptotic behavior is more involved: two correlation dimensions show up, giving rise to a non-smooth behavior of the associated asymptotic exponent. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a third-order dynamical system for finding zeros of the sum of two generalized operators in a Hilbert space H . We establish the existence and uniqueness of the trajectories generated by the system under appropriate continuity conditions, and prove exponential convergence to the unique zero when the sum of the operators is strongly monotone. Additionally, we derive an explicit discretization of the dynamical system, which results in a forward–backward algorithm with double inertial effects and larger range of stepsize. We establish the linear convergence of the iterates to the unique solution using this algorithm. Furthermore, we provide convergence analysis for the class of strongly pseudo-monotone variational inequalities. We illustrate the effectiveness of our approach by applying it to structured optimization and pseudo-convex optimization problems. [ABSTRACT FROM AUTHOR]

Based on the traditional steel spring floating slab track, a quasi-zero-stiffness magnetorheological damping (MRD) track system is constructed by introducing the horizontal spring negative stiffness mechanism and MRD. First, the mechanical model of the system is established, the static analysis is done, and the effects of each parameter on the nonlinear behaviors of the system are numerically analyzed. Then, the dynamics equation of system is set up; subsequently, the amplitude–frequency response equation is obtained by means of the average method. The influences of different parameters on the dynamic response of the system are analyzed. Finally, three semi-active control methods, PID control, fuzzy-PID control and frequency + fuzzy-PID control, are designed, and then, the vibration reduction effect of each control method is simulated. The results present that the proposed system has good vibration isolation effect in low frequency region and a high bearing capacity. The larger nonlinear coefficient, vertical damping ratio, horizontal damping ratio, Coulomb damping force, viscous damping ratio and input current are beneficial to improve the low frequency vibration of the system. By adopting the frequency + fuzzy-PID control method, the peak of force transmissibility and the initial vibration isolation frequency are reduced by 61.9 and 14.2%, respectively, compared with that of the uncontrolled system. The proposed system presents good vibration isolation performance outside the frequency range of 1–3 Hz. [ABSTRACT FROM AUTHOR]

Dynamical properties of a generalized max-plus model for ultradiscrete limit cycles are investigated. This model includes both the negative feedback model and the Sel'kov model. It exhibits the Neimark–Sacker bifurcation, and possesses stable and unstable ultradiscrete limit cycles. The number of discrete states in the limit cycles can be analytically determined and its approximate relation is proposed. Additionally, relationship between the max-plus model and the two-dimensional normal form of the border collision bifurcation is discussed. [ABSTRACT FROM AUTHOR]

The diversity of transmission modes and the heterogeneity of populations in the transmission of infectious diseases are issues that have to be faced in the current disease protection. In this paper, an infectious disease model incorporating age structure and horizontal and environmental spread, along with asymptomatic infection, is proposed to describe diversification of disease transmission routes and population heterogeneity. The expression of the basic reproduction number R0$$ {\mathcal{R}}_0 $$ is derived by a linear approximation method, and it is concluded that if R0<1$$ {\mathcal{R}}_0<1 $$, the disease‐free steady state is globally asymptotically stable; if R0>1$$ {\mathcal{R}}_0>1 $$, the model has a unique endemic steady state which is locally asymptotically stable under certain conditions. Further, the uniform persistence of disease is proved using the persistence theory of the infinite‐dimensional dynamical system when R0>1$$ {\mathcal{R}}_0>1 $$. In additional, the issue of optimal control problem according to this model is investigated, and the representation of optimal control with respect to state variables and adjoint variables is obtained which also imply the existence and uniqueness of optimal control. Finally, numerical simulations are carried out to interpret the theoretical results and to discuss the impact of age and control measures in disease transmission. [ABSTRACT FROM AUTHOR]

The goal of this study is to construct a novel iterative method to compute the matrix sign function using a different approach. It is discussed that the new method is globally convergent and asymptotically stable. It achieves the sixth order of convergence and only requires five matrix–matrix multiplications. The obtained results are extended to compute the number of eigenvalues of a matrix in a specified region of the complex plane. This is done by performing appropriate sequence of matrix sign computations. An application of this technique has been discussed in stability analysis of linear time‐invariant dynamic systems in control theory. Numerical results have been given to justify the effectual performance and superiority of the proposed method. Matrices of various sizes have been considered for this purpose. [ABSTRACT FROM AUTHOR]

This scientific article investigates non-increasing functions and their integral properties, shedding light on their behavior. By examining ∫∞ 0 h(s)ds = 1 − l > 0. Furthermore, examining h(t) = ∫ ∞ t E α+1(s)ds about E(t) and T > 0, we establish ∫ ∞ t E α+1(s)ds ≤ T Eα (0)E(t), showing how E(t) influences h(t). For t ≥ T, E α+1(t) follows a power-law decay. Our study unveils a set of inequalities providing insights into these relationships, offering potential applications in control theory, differential equations, and dynamical systems. [ABSTRACT FROM AUTHOR]

Consistent observations across recording modalities, experiments, and neural systems find neural field spectra with 1/f-like scaling, eliciting many alternative theories to explain this universal phenomenon. We show that a general dynamical system with stochastic drive and minimal assumptions generates 1/f-like spectra consistent with the range of values observed in vivo without requiring a specific biological mechanism or collective critical behavior. [ABSTRACT FROM AUTHOR]

In general, dynamic systems of higher dimensions or with more complex nonlinearities exhibit more intricate behaviors. Conversely, it is worthwhile to discuss whether a complex phenomenon persists in simpler systems. This paper investigates a single-degree-of-freedom vibration system with a velocity-dependent stiffness affected by additive noise. Although the underlying deterministic system possesses only one stable equilibrium point, under noise actions, it has the potential for a stochastic P-bifurcation to occur. This bifurcation causes the central peak of the joint probability density function to split into two symmetric peaks. At this stage, the behavior of the system resembles the development of two phantom attractors that deviate from the equilibrium point, causing the system's random states to linger around them for extended periods. The effects of the damping ratio and noise intensity on the phantom attractors are discussed, together with the critical parameter curve associated with the onset of phantom attractors. Moreover, the generation mechanism of phantom attractors is disclosed by investigating the phase trajectories of the underlying conservative system. The distribution law of those critical parameter values is also proven by the stochastic averaging method, which is associated with the most probable amplitude. This study highlights that phantom attractors can manifest in dynamic systems even in the absence of Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Bifurcations of nonlinear and supernonlinear ion-acoustic waves (IAWs) are studied in an electron-ion plasmas with generalized (r, q)-distributed electrons. The IAWs are examined under the Zakharov–Kuznetsov (ZK) and modified ZK equations using the reductive perturbation technique. Transforming both the ZK and mZK equations into their corresponding dynamical systems, all possible phase spaces and potential energy functions are analyzed. The nonlinear periodic and solitary wave solutions are obtained under the ZK and mZK equations. A newly discovered supernonlinear wave, in particular, supernonlinear periodic wave under the modified ZK equation in electron-ion magnetized plasma with (r, q)-distributed electrons is reported for the first time in the literature. Nonlinear and supernonlinear wave solutions are shown under the influence of physical parameters. The proposed study contributes to new wave motions in slow solar wind streams and astrophysical plasmas. [ABSTRACT FROM AUTHOR]

The hypothalamic–pituitary–adrenal axis is an extremely dynamic system with a combination of both circadian and ultradian oscillations. This state of 'continuous dynamic equilibration' provides a platform that is able to anticipate events, is sensitive in its response to stressors, remains robust during perturbations of both the internal and external environments and shows plasticity to adapt to a changed environment. In this review, we describe these oscillations of glucocorticoid (GC) hormones and why they are so important for GC‐dependent gene activation in the brain and liver, and their consequent effects on the regulation of synaptic and memory function as well as appetite control and metabolic regulation. Abnormalities of mood, appetite and metabolic regulation are well‐known consequences of GC therapy, and we suggest that the pattern of GC treatment and hormone replacement should be a much higher priority for endocrinologists and the pharmaceutical industry. One of the major impediments to our research on the importance of these cortisol rhythms in our patients has been our inability to measure repeated levels of hormones across the day in patients in their home or work surroundings. We describe how new wearable methodologies now allow the measurement of 24‐h cortisol profiles – including during sleep – and will enable us to define physiological normality and allow us both to develop better diagnostic tests and inform, at an individual patient level, how to improve replacement therapy. [ABSTRACT FROM AUTHOR]

Cyclodextrins, commonly used as excipients in antifungal formulations to improve the physicochemical properties and availability of the host molecules, have not been systematically studied for their effects and bioactivity without a complex active substance. This paper evaluates the effects of various cyclodextrins on the physiology of the test organism Candida boidinii. The research examines their impact on yeast growth, viability, biofilm formation and morphological changes. Native ACD, BCD, randomly methylated α- and β-CD and quaternary ammonium α-CD and β-CD were investigated in the 0.5–12.5 mM concentration range in both static and dynamic systems. The study revealed that certain cyclodextrins exhibited notable antifungal effects (up to ~69%) in dynamic systems; however, the biofilm formation was enhanced in static systems. The magnitude of these effects was influenced by several variables, including the size of the internal cavity, the concentration and structure of the cyclodextrins, and the contact time. Furthermore, the study found that CDs exhibited distinct effects in both static and dynamic systems, potentially related to their tendency to form aggregates. The findings suggest that cyclodextrins may have the potential to act as antifungal agents or growth promoters, depending on their structure and surrounding environments. [ABSTRACT FROM AUTHOR]

We investigate a coupled quintessence cosmological model in which a dark-energy scalar field with an exponential potential interacts directly with a dark-matter fluid through a dissipative term inspired by warm inflation. The evolution equations of this model give rise to a three-dimensional dynamical system for which a thorough qualitative analysis is performed for all values of the relevant parameters. We find that the model is able to replicate the observed sequence of late-time cosmological eras, namely, a long enough matter-dominated era followed by a present era of accelerated expansion. In situations where there is a significant transfer of energy from dark energy to dark matter, temporary scaling-type solutions may arise, but, asymptotically, all solutions are dominated by dark energy. [ABSTRACT FROM AUTHOR]

To address the problems of large sliding mode chatter and phase delay in the traditional first-order flux sliding mode observer, a HOT FSMO (High-Order Terminal Flux Sliding Mode Observer) based on an improved tracking differentiator is proposed in this study. A high-order sliding mode control law is designed to achieve chatter suppression of flux linkage estimation, and a new tracking differentiator with low chatter containing a terminal attractor is combined to replace the conventional low pass filter to achieve accurate tracking of the flux linkage and rotor position, as well as filtering functions. The experimental results show that the HOT FSMO based on the novel tracking differentiator can effectively reduce the sliding mode chattering and decrease the position estimation error, while speeding up the system response and improving the system dynamic performance under different speed and load conditions when compared with the traditional linear flux linkage sliding mode observer. [ABSTRACT FROM AUTHOR]

The memristor, a novel device, has been widely utilized due to its small size, low power consumption, and memory characteristics. In this paper, we propose a new three-dimensional discrete memristor map based on coupling a one-dimensional chaotic map amplifier with a memristor. Firstly, we analyzed the memristor model to understand its characteristics. Then, a Simulink model for this three-dimensional discrete memristor map was developed. Lastly, the complex dynamical characteristics of the system were analyzed via equilibrium points, bifurcation diagrams, Lyapunov exponent spectra, complexity, and multistability. This study revealed the phenomena of coexisting attractors and hyperchaotic attractors. Simulink modeling confirmed that the discrete memristors effectively enhanced the chaos complexity in the three-dimensional discrete memristor map. This approach addresses the shortcomings of randomness, the lack of ergodicity, and the small key space in a one-dimensional chaotic map, thereby enriching the theoretical analysis and circuit implementation of chaos. [ABSTRACT FROM AUTHOR]

In this paper, we present a new class of extended oscillators in light of chaos theory. It is based on dynamical complex systems built on the concept of self-describing with a stopping criterion process. We offer an effective studying approach with a specific focus on learning, provoking students' thinking through the triad of enigmatics–creativity–acmeology. Dynamic processes are the basis of mathematical modeling; thus, we can reach the goal of the above-mentioned triad by the proposed differential systems. The results we derive strongly confirm the presence of symmetry in the outcomes of the proposed models. We suggest a stochastic approach to structuring the proposed dynamical systems by modeling the coefficients that drive them by some discrete probability distribution that exhibits symmetry or asymmetry. We propose specific tools for researching the behavior of these systems. [ABSTRACT FROM AUTHOR]

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC-HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size of the linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-like systems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function, and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven model identification algorithms, particularly when applied to commonly used Lorenz time series data. [ABSTRACT FROM AUTHOR]

This study presents a Bayesian maximum a posteriori (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties, and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint MAP and variational Bayesian approximation, are compared to the least absolute shrinkage and selection operator (LASSO), ridge regression, and the sparse identification of nonlinear dynamics (SINDy) algorithms for sparse regression by application to several dynamical systems with added Gaussian or Laplace noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or "Gaussian norm" | | y − y ^ | | M − 1 2 = (y − y ^) ⊤ M − 1 (y − y ^) , where y is a vector variable, y ^ is its estimator, and M is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection for the different systems and noise models examined. [ABSTRACT FROM AUTHOR]

Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the polynomial and exponential convergence rates of the weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to the quasiperiodic and almost periodic dynamical systems respectively, under certain balance between the nonresonant condition and the decay rate of the Fourier coefficients. Diophantine rotations with finite and infinite dimensions are provided as examples. For the first time, we prove the universality of exponential convergence and arbitrary polynomial convergence in the quasiperiodic case and almost periodic case under analyticity respectively. [ABSTRACT FROM AUTHOR]

In [A. Radhakrishnan, M. Belkin and C. Uhler, Overparameterized neural networks implement associative memory, Proc. Natl. Acad. Sci. USA 117(44) (2020) 27162–27170], the authors empirically show that autoencoders trained with standard SGD methods form basins of attraction around their training data. We consider network functions of width not exceeding the input dimension and prove that in this situation, such basins of attraction are bounded and their complement cannot have bounded components. Our conditions in these results are met in several experiments reported in [A. Radhakrishnan, M. Belkin and C. Uhler, Overparameterized neural networks implement associative memory, Proc. Natl. Acad. Sci. USA 117(44) (2020) 27162–27170] and we thus address a question posed therein. We also show that under some more restrictive conditions, the basins of attraction are path-connected. The necessity of the conditions in our results is demonstrated by means of examples. [ABSTRACT FROM AUTHOR]

This review examines complexity science in the context of Heliophysics, describing it not as a discipline, but as a paradigm. In the context of Heliophysics, complexity science is the study of a star, interplanetary environment, magnetosphere, upper and terrestrial atmospheres, and planetary surface as interacting subsystems. Complexity science studies entities in a system (e.g., electrons in an atom, planets in a solar system, individuals in a society) and their interactions, and is the nature of what emerges from these interactions. It is a paradigm that employs systems approaches and is inherently multi- and cross-scale. Heliophysics processes span at least 15 orders of magnitude in space and another 15 in time, and its reaches go well beyond our own solar system and Earth's space environment to touch planetary, exoplanetary, and astrophysical domains. It is an uncommon domain within which to explore complexity science. After first outlining the dimensions of complexity science, the review proceeds in three epochal parts: 1) A pivotal year in the Complexity Heliophysics paradigm: 1996; 2) The transitional years that established foundations of the paradigm (1996-2010); and 3) The emergent literature largely beyond 2010. This review article excavates the lived and living history of complexity science in Heliophysics. It identifies five dimensions of complexity science, some enjoying much scholarship in Heliophysics, others that represent relative gaps in the existing research. The history reveals a grand challenge that confronts Heliophysics, as with most physical sciences, to understand the research intersection between fundamental science (e.g., complexity science) and applied science (e.g., artificial intelligence and machine learning (AI/ML)). A risk science framework is suggested as a way of formulating the grand scientific and societal challenges in a way that AI/ML and complexity science converge. The intention is to provide inspiration, help researchers think more coherently about ideas of complexity science in Heliophysics, and guide future research. It will be instructive to Heliophysics researchers, but also to any reader interested in or hoping to advance the frontier of systems and complexity science. [ABSTRACT FROM AUTHOR]

Travelling waves in circuit chains are studied to measure continuous dispersion. A lock‐in frequency meter (LIF) is suitable for precisely determining k for each set ω$\omega $ of waves in finite alternate LC chains, where LIF has been proven to be more accurate than the fast Fourier transform. In addition to the ω$\omega $–k measurement, the wave impedance spectrum of the travelling wave can be measured simultaneously, for investigating the dispersion and splitting of pulse propagation. The measured dispersion is validated to be consistent with the derived theoretical equations. The result provides an independent way to precisely obtain dynamical system properties for chains composed of non‐ideal components, such as resistors for researching non‐Hermitian behaviour under dissipation. Systematical mapping of relative deviation dependence of wave dispersion measurement with LIF on different chain length and component variation is studied, indicating boundaries of 1%, 0.1%, and 0.01% precision for guidance of experiments. [ABSTRACT FROM AUTHOR]

This study investigates a class of two-dimensional, two-parameter squared discrete dynamical systems. It determines the conditions for local stability at the fixed points for these proposed systems. Theoretical and numerical analyses are conducted to examine the bifurcation behavior of the proposed systems. Conditions for the existence of Naimark–Sacker bifurcation, transcritical bifurcation, and flip bifurcation are derived using center manifold theorem and bifurcation theory. Results of the theoretical analyses are validated by numerical simulation studies. Numerical simulations also reveal the complex bifurcation behaviors exhibited by the proposed systems and their advantage in image encryption. [ABSTRACT FROM AUTHOR]

The quality of images captured digitally or transmitted over networks is distorted by noise during the process. The current methods of image restoration can be ineffective in dealing with intricate noise patterns or may be slow or imprecise. This paper fills this gap by presenting a new second-order continuous-time dynamical system for denoising of images in image restoration. The approach used in this work poses the problem as a convex quadratic program that can, thus, be solved for optimality. The existence and uniqueness of a global solution are theoretically demonstrated, and the condition for the global strong convergence of the system's trajectory is provided. The method presented in this paper is shown to be useful in a number of experiments on image restoration. As for the performance, it is higher than that of other known algorithms, with an average SNR equal to 34.78 and a Structural Similarity Index Measure (SSIM) of 0.959 for the reconstructed images. Such improvements demonstrate the effectiveness of the second-order dynamical system approach in actual image restoration applications. [ABSTRACT FROM AUTHOR]

The diagonal dominance property has been applied in many different ways and has proven to be very useful in various research areas. Its generalization, also known under the name H-matrix property, can be applied and produce significant benefits in economic theory, environmental sciences, epidemiology, neurology, engineering, etc. For example, it is known that the (local) stability of a (nonlinear) dynamic system is ensured if the (Jacobian) matrix belongs to the H-matrix class, and all its diagonal elements are negative. However, checking the H-matrix property itself is too expensive (from a computational point of view), so it is always worth investing effort in finding new subclasses of H-matrices, defined by relatively simple and practical conditions. Here, we will define a new subclass, which is closely related to the Euclidean vector norm, give some possible applications of this new class, and consider its relationship to some known subclasses. [ABSTRACT FROM AUTHOR]

The dynamics of mastering the degrees of freedom in motor learning are still far from being understood. The present work explored coordination dynamics in a redundant task, relating it to performance and adaptation in a serial stimulus tracking task. One hundred and sixty-three children (10–14 years of age) continuously responded to sequential stimuli (containing five stimuli) by pressing the respective sensors before the next stimulus presentation. Participants performed 120 trials with a fixed sequence (4–2–5–3–1) and a fixed interstimuli interval (800 ms) to learn the first pattern (practice phase). Then, a changed sequence (4–2–5–1–3) with a shorter interval (700 ms) was presented for 40 trials (adaptation phase). To measure coordination and its change, we calculated the correlation matrix of the stimulus–touch interval between the five sensors in blocks of 20 trials of the practice phase and classified individuals in terms of clusters. We found associations between coordination dynamics, performance curves, and adaptation in both coordination and performance. Furthermore, using network analyses, we found a tendency for all groups to increase the clustering coefficient. We discuss the possibility of this result representing a process of progressive segregation. [ABSTRACT FROM AUTHOR]

Summary: The d‐q detection method based on instantaneous reactive power theory (IRPT) is one of the commonly used time‐domain analysis methods for harmonic detection. Due to the poor dynamic performance of the algorithm caused by the low pass filter (LPF) in the d‐q detection method, an improved series repetitive control (ISRC) structure is proposed in this paper. Using attenuation factor and correction factor to improve the series repetitive controller, the ISRC contains a negative resonance peak with a peak value of 150 dB at the 6 k harmonic frequency, and the amplitude gain is 0 dB at frequencies outside the 6 k harmonic frequency. Therefore, ISRC can achieve good attenuation effect on 6 k harmonics while maintaining the same gain at other frequencies. ISRC is used instead of LPF in the traditional d‐q detection and this strategy improves the dynamic response of the system while guaranteeing its steady state performance. Finally, simulations and experiments verify the feasibility of the strategy. [ABSTRACT FROM AUTHOR]

Summary: Large‐scale linear time‐invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. Glover developed the Hankel norm approximation (HNA) algorithm for optimally reducing the system in the Hankel norm, and we study its numerical issues. We provide a remedy for the numerical instabilities of Glover's HNA algorithm caused by clustered singular values. We analyze the effect of our modification on the degree and the Hankel error of the reduced system. Moreover, we propose a two‐stage framework to reduce the order of a large‐scale LTI system given samples of its transfer function for a target degree k$$ k $$ of the reduced system. It combines the adaptive Antoulas–Anderson (AAA) algorithm, modified to produce an intermediate LTI system in a numerically stable way, and the modified HNA algorithm. A carefully computed rational approximation of an adaptively chosen degree d$$ d $$ gives us an algorithm for reducing an LTI system, which achieves a balance between speed and accuracy. [ABSTRACT FROM AUTHOR]

The dynamic vibration absorber with inerter and grounded stiffness (IG-DVA) is used to control a two-scale system subject to a weak periodic perturbation. The vibration suppression effect is remarkable. The amplitude of the main system coupled with absorber is significantly reduced, and the high frequency vibration completely disappears. First, through the slow-fast analysis and stability theory, it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system. After adding the dynamic vibrator absorber, the center in the autonomous system changes to an asymptotically stable focus, consequently suppressing the vibration in the non-autonomous system. Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system, thereby regulating the stability of the system. Transitioning from a qualitative standpoint to a quantitative approach, a comparison of the solutions before and after the introduction of the dynamic absorber reveals that, when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal, the high-frequency part in the analytical solution disappears. As a result, this leads to a reduction in the amplitude of the trajectory, achieving a vibration reduction effect. [ABSTRACT FROM AUTHOR]

Models are often employed to integrate knowledge about epidemics across scales and simulate disease dynamics. While these approaches have played a central role in studying the mechanics underlying epidemics, we lack ways to reliably predict how the relationship between virulence (the harm to hosts caused by an infection) and transmission will evolve in certain virus-host contexts. In this study, we invoke evolutionary invasion analysis—a method used to identify the evolution of uninvadable strategies in dynamical systems—to examine how the virulence-transmission dichotomy can evolve in models of virus infections defined by different natural histories. We reveal peculiar patterns of virulence evolution between epidemics with different disease natural histories (SARS-CoV-2 and hepatitis C virus). We discuss the findings with regards to the public health implications of predicting virus evolution, and in broader theoretical canon involving virulence evolution in host-parasite systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a differential equation across both space and time with the aim of recovering critical data, such as initial values, the sources, the driving operator, or other relevant details. Our focus in this study is the recovery of unknown, stationary sources across both space and time, leveraging space-time samples. This research may have significant applications; for instance, it could provide a model for strategically placing devices to measure the number of pollutants emanating from factory smokestacks and dispersing across a specific area. Space-time samples could be collected using measuring devices placed at various spatial locations and activated at different times. We present necessary and sufficient conditions for the positioning of these measuring devices to successfully resolve this dynamical sampling problem. This paper provides both a theoretical foundation for the recovery of sources in dynamical systems and potential practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new passivity‐based controller design technique for discrete‐time fully actuated systems. The controller establishes finite‐time and fixed‐time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non‐asymptotic stabilization. A numerical example to validate the proposed methods is provided. [ABSTRACT FROM AUTHOR]

Objectives: Cardiac motion artifacts hinder the assessment of coronary arteries in coronary computed tomography angiography (CCTA). We investigated the impact of motion compensation reconstruction (MCR) on motion artifacts in CCTA at various heart rates (HR) using a dynamic phantom. Materials and methods: An artificial hollow coronary artery (5-mm diameter lumen) filled with iodinated contrast agent (400 HU at 120 kVp), positioned centrally in an anthropomorphic chest phantom, was scanned using a dual-layer spectral detector CT. The artery was translated at constant horizontal velocities (0–80 mm/s, increment of 10 mm/s). For each velocity, five CCTA scans were repeated using a clinical protocol. Motion artifacts were quantified using the in-plane motion area. Regression analysis was performed to calculate the reduction in motion artifacts provided by MCR, by division of the slopes of non-MCR and MCR fitted lines. Results: Reference mean (95% confidence interval) motion artifact area was 24.9 mm2 (23.8, 26.0). Without MCR, motion artifact areas for velocities exceeding 20 mm/s were significantly larger (up to 57.2 mm2 (40.1, 74.2)) than the reference. With MCR, no significant differences compared to the reference were shown for all velocities, except for 70 mm/s (29.0 mm2 (27.0, 31.0)). The slopes of the fitted data were 0.44 and 0.04 for standard and MCR reconstructions, respectively, resulting in an 11-time motion artifact reduction. Conclusion: MCR may improve CCTA assessment in patients by reducing coronary artery motion artifacts, especially in those with elevated HR who cannot receive beta blockers or do not attain the targeted HR. Clinical relevance statement: This vendor-specific motion compensation reconstruction may improve coronary computed tomography angiography assessment in patients by reduction of coronary artery motion artifacts, especially in those with elevated various heart rates (HR) who cannot receive beta blockers or do not attain the targeted HR. Key Points: • Motion artifacts are known to hinder the assessment of coronary arteries on coronary CT angiography (CCTA), leading to more non-diagnostic scans. • This dynamic phantom study shows that motion compensation reconstruction (MCR) reduces motion artifacts at various velocities, which may help to decrease the number of non-diagnostic scans. • MCR in this study showed to reduce motion artifacts 11-fold. [ABSTRACT FROM AUTHOR]

Summary: The control problem of the hypersonic vehicles is studied in this article. A new control approach is presented. This approach consists of a data‐driven dynamic model established by multiple neural networks, an online identification method for system parameters, and a basic backstepping controller. The implementation of this approach requires a dynamic model and system parameters including the moment of inertia and aerodynamic parameters of the hypersonic vehicles. The parameter identification problem is regarded as a dynamic optimization process. The loss function is designed by the Lagrange criterion, and its constraints are determined by the physical and the numerical values. In the case of model mutation, the system parameters identified online are used as the nominal values of the output of the neural network in the data‐driven model to adjust the controller through its gradient descent. Simulation comparisons are given to show the effectiveness of the proposed data‐driven approach. [ABSTRACT FROM AUTHOR]

Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal interpolation points and the appropriate size of the reduced-order model. An approach that addresses the first problem for linear, unstructured systems is the iterative rational Krylov algorithm (IRKA), which computes optimal interpolation points through iterative updates by solving linear eigenvalue problems. However, in the case of preserving internal system structures, optimal interpolation points are unknown, and heuristics based on nonlinear eigenvalue problems result in numbers of potential interpolation points that typically exceed the reasonable size of reduced-order systems. In our work, we propose a projection-based iterative interpolation method inspired by IRKA for generally structured systems to adaptively compute near-optimal interpolation points as well as an appropriate size for the reduced-order system. Additionally, the iterative updates of the interpolation points can be chosen such that the reduced-order model provides an accurate approximation in specified frequency ranges of interest. For such applications, our new approach outperforms the established methods in terms of accuracy and computational effort. We show this in numerical examples with different structures. [ABSTRACT FROM AUTHOR]

Reliability-based control co-design (RBCCD) formulations have been developed for the design of stochastic dynamic systems. To address the limitations of their current formulations, and to enable higher-fidelity solutions for complex problems, a novel reliability-based multidisciplinary feasible (MDF) formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) and a new reliability analysis method using generalized polynomial chaos (gPC) expansion for RBCCD were developed in previous work. Although the gPC expansion method was initially selected for the reliability analysis of simulation-based RBCCD, its performance against state-of-the-art, the most-probable-point (MPP) method, has not been established yet. Therefore, in this work, the first-ever MPP-based formulations of RB-MDF-MDSDO are developed, and using two engineering test problems, the new formulations' solution efficiency and accuracy are compared to those from the gPC-based formulation. Numerical results reveal that the gPC expansion method is marginally more accurate than the MPP algorithms, and therefore, it is more suitable for accuracy-sensitive applications. Conversely, the MPP algorithms are much more efficient, and thus, are more attractive for problems where solution efficiency is the priority. [ABSTRACT FROM AUTHOR]

In this study, we investigate the Biswas–Arshed (BA) model, applicable in various fields such as fluid mechanics, laser science, and nonlinear optics. We employ the direct algebraic procedure, the modified rational sine–cosine process, and the 1 G ′ approach to obtain soliton dynamics of the mentioned model. Chaotic behavior and sensitivity analysis of the BA model are also investigated using a planar dynamic system. As a result, periodic, quasi-periodic, and chaotic patterns are obtained from the suggested nonlinear model. We also obtain various soliton solutions from this model with novel properties. From the proposed equation, we can obtain periodic waves with bright solitons, bright-dark solitons, dark solitons, breather waves with singularities, double periodic waves, periodic waves with singularities, bright solitons with singularities, multiple bright dark breather waves with singularities, and multiple bright breather waves with singularities. Certain features of the outcomes are exhibited in 2D, 3D, and density views. The work presented is innovative as it offers valuable insights into the governing model's intricate behaviors and diverse waveforms through extensive analysis. This study also contributes to understanding real-world problems by incorporating waveform properties, bifurcation analysis, chaotic dynamics, and sensitivity tests. [ABSTRACT FROM AUTHOR]

The primary aim of this study is to examine the deep characteristics of the Shynaray-IIA equation by applying the improved generalized Riccati equation mapping approach. We derive a dynamical system that is effectively linked to the equation by using the Galilean transformation. Next, we analyze the bifurcation mechanisms in this derived system by applying principles from planar dynamical systems theory. We conducted a thorough investigation of the probable occurrence of chaotic behaviors by introducing a perturbed term into the dynamical system and systematically studying the Shynaray-IIA equation. The inclusion of a thorough two-phase portrayal deepens the scope of this study. We utilized the Runge–Kutta method to thoroughly examine the sensitivity of the dynamical system. The analytical technique allowed us to confirm that slight perturbations in the initial conditions have little impact on the stability of the solution. Furthermore, the advanced technique of utilizing the improved generalized Riccati equation mapping approach is utilized to obtain new exact solutions for the Shynaray-IIA model. We exhibit visual outcomes for individual solutions, providing a comprehensive evaluation by showcasing different results using MATLAB across several dimensions. These solutions and chaotic analysis will be of high significance in all areas of applications of shynaray IIA equation such as optical communications, tsunami and tidal wave phenomena. [ABSTRACT FROM AUTHOR]

This manuscript studies the exact solitary wave profiles for the conformable Schrödinger–Poisson dynamical system. This system has a significant role in gravity's quantum state operation approximates the interaction between quantum mechanics and gravitation. The diverse exact solitary wave profiles are constructed by using the Khater method. The different closed-form solutions are obtained such as dark, singular, hyperbolic, periodic, and plane waves. Moreover, the modulation instability is also discussed for this dynamical system. To, show the physical significance of desired results we plot the 3D and 2D plots along with the related contour graphs, which are also drawn. The constraint criteria for the exact solutions are also exposed. [ABSTRACT FROM AUTHOR]

This paper is dedicated to exterminate the ( 2 + 1 )-dimensional integro-differential Jaulent–Miodek equation, a prominent model linked to energy-dependent Schrödinger potential. This equation is employed in a wide array of disciplines, including fluid dynamics, condensed matter physics, optics, and various engineering systems. First, we are given to derive exact wave solutions for the ( 2 + 1 )-dimensional integro-differential Jaulent–Miodek equation using an innovative approach known as the new modified unified auxiliary equation method. We offer a comprehensive visual representation and some exact solutions propagate of these solutions in 2D and 3D plots, using various parametric values for a comprehensive analysis. In addition, we employed the planar dynamical system method to study phase portraits and chaotic behavior of the governing equation. Through the analysis of phase portraits, the sensitivity of dynamic system is examined. The chaotic behavior of dynamic system is examined by time series, Poincaré section, and 2D, 3D phase portraits. [ABSTRACT FROM AUTHOR]

The advent of machine learning has led to innovative approaches in dealing with clinical data. Among these, Neural Ordinary Differential Equations (Neural ODEs), hybrid models merging mechanistic with deep learning models have shown promise in accurately modeling continuous dynamical systems. Although initial applications of Neural ODEs in the field of model‐informed drug development and clinical pharmacology are becoming evident, applying these models to actual clinical trial datasets—characterized by sparse and irregularly timed measurements—poses several challenges. Traditional models often have limitations with sparse data, highlighting the urgent need to address this issue, potentially through the use of assumptions. This review examines the fundamentals of Neural ODEs, their ability to handle sparse and irregular data, and their applications in model‐informed drug development. [ABSTRACT FROM AUTHOR]

Static and dynamic metamaterials have been extensively studied for their ability to manipulate different physical fields and directed to broad applications. Because the governing equations of heat transfer consist of nonlinear terms with conservation of mass, momentum and energy, the equations can exhibit elliptical, parabolic, hyperbolic and hybrid configurations under different transfer modes. Such multi-mode transfer characteristics intrinsically make thermal metamaterials distinguish themselves from other metamaterials with unique static and dynamic manipulation mechanisms. Therefore, numerous studies have emerged that use the transformation theory and other methods to control static thermal metamaterials. It leads to the development of thermal cloaks, thermal concentrators, thermal diodes, and so on. Originating from the static style, the manipulation of heat transfer has expanded to dynamic systems in recent years. The introduction of hydrodynamics in metamaterial design leads to numerous novel physics effects, such as dynamic cloaking, zero-drag characteristics, topological heat transfer, nonreciprocal diffusion, and non-Hermitian physics. Moreover, the dynamic thermal metamaterials allow accurate control at both time and space dimensions, leading to exciting applications such as adjustable, reconfigurable, and intelligent thermal meta-devices. However, few studies have systematically analyzed thermal metamaterials from the perspective of static and dynamic manipulation. In this review, we aim at clarifying the connection and distinction of static and dynamic manipulation from the scopes of principle, application, and physical effects. We start with the development of static thermal metamaterials and its application. Subsequently, the development of dynamic thermal metamaterials is presented both in fundamental theory and application. Finally, we summarize the research directions and prospect future research challenges for static and dynamic thermal metamaterials. [ABSTRACT FROM AUTHOR]

Assume that (Y , ρ) is a nontrivial complete metric space, and that (Y , g 1 , ∞) is a time-varying discrete dynamical system (T-VDDS), which is given by sequences (g l) l = 1 ∞ of continuous selfmaps g l : Y → Y . In this paper, for a given Furstenberg family G and a given T-VDDS (Y , g 1 , ∞) , G -scrambled pairs of points of the system (Y , g 1 , ∞) (which contains the well-known scrambled pairs) are provided. Some properties of the set of G -scrambled pairs of a given T-VDDS (Y , g 1 , ∞) are studied. Moreover, the generically G -chaotic T-VDDS and the generically strongly G -chaotic T-VDDS are defined. A sufficient condition for a given T-VDDS to be generically strongly G -chaotic is also presented. [ABSTRACT FROM AUTHOR]

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system's parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results. [ABSTRACT FROM AUTHOR]

Uncertainty can lead to jitter or overshoot in mechanical systems, necessitating the design of multiple constraints to stabilize them. This paper proposes a control structure based on the generalized Udwadia–Kalaba equation to address these constraints simultaneously. An uncertain dynamical model is developed, incorporating both equality and inequality constraints. By integrating diffeomorphism theory, a robust control strategy is designed to ensure compliance with these constraints. Utilizing the Lyapunov approach, the uniform boundedness and uniform ultimate boundedness of the dynamical system are demonstrated. Finally, the feasibility of the proposed control method is validated through its application to a belt conveyor system. • Equality constraints and inequality constraints are simultaneously considered in dynamical system based on the generalized Udwadia–Kalaba approach. • A robust control for handling inequality constraints that does not affect equality constraints is designed. • The robust control can render the uncertain system uniformly bounded and uniformly ultimately bounded. • The method is proposed of applying inequality constraints to belt conveyors to avoid belt breakage and folding faults in engineering. [ABSTRACT FROM AUTHOR]

We consider time-dependent perturbations of integrable and near-integrable Hamiltonians. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of biasymptotically quasi-periodic solutions. That is, orbits converging to some quasi-periodic solutions in the future (as ) and the past (as ). Concerning the proof, thanks to the implicit function theorem, we prove the existence of a family of orbits converging to some quasi-periodic solutions in the future and another family of motions converging to some quasi-periodic solutions in the past. Then, we look at the intersection between these two families when . Under suitable hypotheses on the Hamiltonian's regularity and the perturbation's smallness, it is a large set, and each point gives rise to biasymptotically quasi-periodic solutions. [ABSTRACT FROM AUTHOR]

Controlling the growth of bacterial biofilms in a specific pattern greatly enhances the study of cell‐to‐cell interactions and paves the way for expanding their biological applications. However, the development of simple, cost‐effective, and highly resolved biopatterning approaches remains a persistent challenge. Herein, a pioneering photodynamic biopatterning technique for the creation of living bacterial biofilms with customized geometries at high resolutions is presented. First of all, an outstanding aggregation‐induced emission photosensitizer is synthesized to enable efficient photodynamic bacterial killing at a low concentration. By combining with custom‐designed photomasks featuring both opaque and transparent patterns, the viability of photosensitizer‐coated bacteria is successfully manipulated by controlling the degree of light transmittance. This process leads to the formation of living bacterial biofilms with specific patterns replicated from the photomask. Such an innovative strategy can be employed to generate living bacterial biofilms composed of either mono‐ or multispecies, with a spatial resolution of approximately 24 µm. Furthermore, its potential applications in information storage/encryption and antibiotic screening are explored. This study provides an alternative way to understand and investigate the intricate interactions among bacteria within 3D biofilms, holding great promise in the controlled fabrication of dynamic biological systems for advanced applications. [ABSTRACT FROM AUTHOR]

In recent years, the cost-effectiveness and versatility of Unmanned Aerial Vehicles (UAVs) have led to their widespread adoption in both military and civilian applications, particularly for operations in remote or hazardous environments where human intervention is impractical. The use of multi-agent UAV systems has notably increased for complex tasks such as surveying and monitoring, driving extensive research and development in control, communication, and coordination technologies. Evaluating and analysing these systems under dynamic flight conditions present significant challenges. This paper introduces a mathematical model for leader–follower structured Quadrotor UAVs that encapsulates their dynamic behaviour, incorporating a novel multi-agent ad hoc coordination network simulated via COOJA. Simulation results with a pipeline surveillance case study demonstrate the efficacy of the coordination network and show that the system offers various improvements over contemporary pipeline surveillance approaches. [ABSTRACT FROM AUTHOR]

Ecosystems contain numerous species interacting with each other and the environment. However, data on all relevant state variables is rarely available, hampering inference and prediction. Empirical dynamic modelling (EDM) is a valuable tool for prediction, inference and control in such partially observed systems.However, EDM typically assumes that the available time series are observed without error. Failing to account for observation noise strongly biases estimates of Lyapunov exponents and reduces forecast accuracy. To address this limitation, we propose incorporating EDM into a hidden Markov framework and using an iterative scheme based on the expectation maximization (EM) algorithm to obtain filtered state and parameter estimates.We evaluate the performance of this approach on several simulated dynamical systems with a range of additive noise levels, as well as on insect population time series.Accounting for observation noise improved accuracy of population forecasts and estimates of Lyapunov exponents (LE) over a wide range of noise levels relevant to ecological time series. [ABSTRACT FROM AUTHOR]