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• The citations of 729,515 articles fit by the generalized extreme-value distribution. • The complexity of references and citations of papers' quantiles is studied. • The macroscopic model of the citation distribution is proposed. The paper presents an in-depth study of uncited papers. For that, we explore the documents indexed in the INSPIRE database from 1970 to 2015. Uncited articles represent a complex bibliometric environment in which references are generated. The reference lists of uncited papers form a dynamic system partially responsible for the redistribution of scientific impact. Our task is to quantify the detailed structure of citations and references directly in terms of quantiles. We also study the entropy and the statistical complexity measure of references and citations of papers' quantiles. We introduce a theoretical framework in which citation distribution is considered an asymptotic distribution of the largest values in a sequence of independent identically distributed random variables. We show that this asymptotic distribution is the generalized extreme-value distribution. Furthermore, we empirically demonstrate that the asymptotic behavior of citation distribution is close to (but not quite) the generalized extreme-value distribution. [ABSTRACT FROM AUTHOR]

Abstract: Five ratios R H , R T , S H , S T and S Z derived from the three-part division of a set of sources in h-core, h-tail and uncited sources are defined. Dynamic changes in the three independent ratios R H , S H and S Z are studied for six selected topics. Data about these topics are obtained from the Web of Science for scientific papers and Derwent Innovations Index for technical patents. It is observed that all R H - and S H -values decrease when the time span widens, while S Z stays the same or increases; and that all R H - and S H -values for papers are larger than the corresponding values for patents. The shifted Lotka distribution is used in a theoretical interpretation of these empirical phenomena. [Copyright &y& Elsevier]

The design of a high-volume printer for professional use is rather complex. The design of the paper path and the timing of sheets is frequently reengineered as the design of the printer components progresses. This paper presents an optimization model for the combined paper path and timing design problem. The paper path is an optimal physical dimensioning problem, while the timing is an open-loop optimal control problem. The coupled optimization problem is formulated as a simultaneous analysis and design (SAND) problem using a direct transcription of the optimal control problem. Benefits of the chosen formulation for industrial application are the ease of setting up the optimization model for arbitrary printer configurations, and the short computation times. Results of an industrial case are presented. [ABSTRACT FROM AUTHOR]

Identification of the mechanisms which permit ecological communities to maintain high levels of biodiversity is of both theoretical interest and practical importance. Intransitive competition, in which there is no single superior competitor, is known to play an important role in this problem. In this study, we undertake a systematic comparative analysis of how different competition modes and ranges affect community stability in paper–rock–scissors games. We confirm that short-ranged interactions, in combination with cyclic competition, permits relatively stable coexistence. However, in contrast to previous studies, we show that long-range interactions can also produce stable communities. This stability emerges when competition interactions create asymmetries in the opportunities for population growth depending on the abundance of the species. Our findings demonstrate that small differences in the way species compete can qualitatively change dynamic behaviours of the system, and therefore emphasize the importance of correctly identifying these competition modes when designing conservation actions. • We compare system stability among four interaction modes in cyclic competition. • We find that long-ranged competition can also produce stable coexistence. • Small differences in interaction modes qualitatively change dynamic behaviours. • We emphasize the importance of correctly identifying species competition modes. [ABSTRACT FROM AUTHOR]

This Special Issue of Applied Mathematical Modelling journal consists of selected quality papers originally presented at 15th International Conference "Dynamical Systems - Theory and Applications" (DSTA) which took place on December 2-5, 2019 in Lodz, Poland. B Dzyubak et al. b analysed a non-linear multi-scale diffusion cancer invasion model that describes the interactions of the tumour cells, matrix-metalloproteinases, matrix-degradative enzymes and oxygen. Chaotic cancer attractors are quantified and multi-parametric evolution of conditions leading to cancer invasion is defined. [Extracted from the article]

In a circular economy, extended producer responsibility (EPR) is a regulatory approach that accounts for all environmental costs associated with a product throughout its life cycle. When considering the EPR, the regulator must (1) design an integrated framework for different stakeholders and (2) provide effective policies to create financial incentives to accelerate the circular system. Recycling funds and subsidies are the most prominent financial strategies that can either encourage or curtail the flows of recycled products. In Indonesia, a few companies provided recycling bonus s to their customers as incentives to increase the recycling rate. However, the recycling rate was not as effective as expected by the enterprise because recycling was practiced by a limited number of companies, rendering it economically unviable. The enterprises hope the government could develop a recycling fund system. In order to develop the recycling fund system, a system dynamic model was proposed and simulated to optimize the recycling funds and subsidies based on decentralized reverse supply chains. Although it is not a novelty model; however, the research show a very significant results for the government in Indonesia. This enabled a more precise, well-planned, and sustainable decision-making process for the EPR. In addition, by utilizing the system dynamic model with different scenarios in a real case study (aseptic paper packaging waste), we found that the capacity of the recycler could become the reference for the funds to be paid by the importer-producer group, wherein the recycling rate will increase with an increase in the recycling fund. • When formulating an EPR scheme, two points must be considered: framework and policies. • A system dynamic model was proposed and simulated to get the optimal solution. • A related case study involving aseptic paper packaging (APP) was considered. [ABSTRACT FROM AUTHOR]

This paper addresses the control of a nonlinear system affected by deadzone effects, using a constrained actuator. The system itself incorporates a second-order oscillatory dynamic actuator, with an unknown nonlinear input-output relationship. The proposed algorithm not only accommodates the deadzone constraints on control inputs but also considers the actuator's saturation limits in control input calculations. It introduces a trajectory tracking mechanism that, instead of directly following the primary trajectory, adheres to an alternative trajectory capable of stable tracking, gradually converging to the main trajectory while accounting for operational constraints. In practical control systems, the actuator's input-output relationship is often nonlinear and unknown, requiring inversion for model-based control. This paper employs an offline-trained neural network trained on synthetic data to identify and approximate the actuator's behavior. To optimize the control system's performance and ensure stability during sudden error changes, the control input operates in two modes: position and velocity control. This dual-mode control allows for continuous switching between the two, facilitated by an innovative optimization technique based on the gradient descent method with a variable step size. Simulation results validate the effectiveness of the proposed algorithm in controlling systems constrained by hard limits and featuring nonlinear oscillatory actuators, providing a valuable contribution to the field of control systems. • Developing a dual mode non-predictive control algorithm based on discrete-time system equations. • Utilizing an offline-trained neural network for estimating the inverse of the nonlinear actuator relationship. • Stable desired trajectory mapping based on inherent and actuation constraints while maintaining asymptotic stability. • Substituting the trajectory within a fixed range outside of the constant deadzone and inside the variable saturation. • Optimized balancing position and velocity control modes through a weighted average of two control forces. [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, the fractional space-time nonlinear Chen-Lee-Liu equation has been considered using various methods. The investigation of the transition from periodic to quasi-periodic behavior has been conducted using a saddle-node bifurcation approach. The paper reports the conditions of multi-dimensional bifurcations of dynamical solutions. Additionally, a direct algebraic method has been used to calculate various 2D and 3D solitonic structures of the equation, and an analysis of their accuracy and effectiveness has been conducted. Furthermore, the Galilean transformation has been used to convert the equation into a planar dynamical system, which is further utilized to obtain bifurcations and chaotic structures. Chaotic structures of perturbed dynamical system are observed and detected through chaos detecting tools such as 2D-phase portrait, 3D-phase portrait, time series analysis, multistability and Lyapunov exponents over time. Further, sensitivity behavior for a range of initial conditions, both perturbed and unperturbed. The results suggest that the investigated equation exhibits a higher degree of multi-stability. [ABSTRACT FROM AUTHOR]

In the context of predicting the behaviour of chaotic systems, Schroer, Sauer, Ott and Yorke conjectured in 1998 that if a dynamical system defined by a smooth diffeomorphism T of a Riemannian manifold X admits an attractor with a natural measure μ of information dimension smaller than k , then k time-delayed measurements of a one-dimensional observable h are generically sufficient for μ -almost sure prediction of future measurements of h. In a previous paper we established this conjecture in the setup of injective Lipschitz transformations T of a compact set X in Euclidean space with an ergodic T -invariant Borel probability measure μ. In this paper we prove the conjecture for all (also non-invertible) Lipschitz systems on compact sets with an arbitrary Borel probability measure, and establish an upper bound for the decay rate of the measure of the set of points where the prediction is subpar. This partially confirms a second conjecture by Schroer, Sauer, Ott and Yorke related to empirical prediction algorithms as well as algorithms estimating the dimension and number of required delayed measurements (the so-called embedding dimension) of an observed system. We also prove general time-delay prediction theorems for locally Lipschitz or Hölder systems on Borel sets in Euclidean space. [ABSTRACT FROM AUTHOR]

A tracking control scheme is proposed for complex dynamic network (CDN), where the CDN is regarded wholly as a dynamic composite system which consists of two mutually coupled subsystems. One subsystem consists of all nodes and the other consists of all links, and consider the weights of the links to be state variables in the latter subsystem. There are two parts in the structure of the proposed tracking control scheme: the designed controller of nodes and the synthesis of the coupling term in links. These two parts can guarantee two subsystems to asymptotically track the given reference targets, respectively. This approach originates from the communication transmission network (CTN). In CTN, for the network optimization management, the reference network topology (NT), such as the star topology, is required as a target for tracking in communication transmission (links) when each node in network needs to track its own target. The control scheme provided of this paper coincides with above requirement. And finally, a comparative simulation example is given for illustrating the effectiveness of the provided control scheme. • The dynamic equations of nodes and NT are represented by the matrix differential equations, this can contain many models in other papers and simplify the control scheme, which is rarely discussed. • The tracking targets of nodes and NT given in this paper are independent of each other, which is novel. • When all nodes track the reference targets, the eventual network layout is shown by the desired NT, which is novel. [ABSTRACT FROM AUTHOR]

The increasing number of man-made objects in near-earth space is becoming a serious problem for future space missions around the Earth. Among the proposed strategies to face this issue, and due to the passive and propellant-less character, electrodynamic tethers appear to be a promising option for spacecraft in low Earth orbits thanks to the limited storage mass and the minimum interface requirements to the host spacecraft. This work presents the roadmap that the Electrodynamic Tether Technology for Passive Consumable-less Deorbit Kit (E.T.PACK) is following to develop a prototype of a deorbit device based on electrodynamic tether technology with Technology Readiness Level 4 by the end of 2022. The paper illustrates the roadmap of the activities carried out at the University of Padova, where software and hardware have been prepared to validate some of the critical elements of the deorbit device. Specifically, the software tools include: (a) the software called "DEPLOY" that allows the computation of a reference trajectory for the deployment of the tether and the completion of sensitivity analysis of the deployment trajectory to key error sources; (b) the software called "FLEXSIM" that predicts the performances of electrodynamic tethers as a function of the system configuration employed; and (c) the software called "FLEX" that includes the dynamical effects of tether flexibility and provides important information on the dynamic stability of the system during deployment and deorbiting phase. The paper describes in detail the three software tools and provides results of a simulation showing how it is possible to deorbit a 24-kg satellite from an initial orbital altitude of 600 km in less than 100 days using a 500-m long tape-like bare tether. The team has also developed laboratory mock-ups and performed experimental activities to: (a) determine the tether mechanical properties; (b) test the functionality of mechanisms used to deploy the tether; (c) test the functionality of the attitude control assembly used during the deployment phase; and (d) validate a passive damper designed for dissipating the longitudinal oscillations of the tether and thus guarantee the stability of the system during both deployment and deorbiting phase. The paper provides a description of both the laboratory setup and the experimental activities performed to validate EDT technologies, including the damping capability of a compact passive-damping mechanism, showing how it can reduce consistently the peak forces up to about 80%. • Optimization of full-length deployment trajectory. • High fidelity simulations of deorbiting with electrodynamic tethers. • Experimental validation of technologies for tape electrodynamic tethers. • Close-proximity deployment testing with frictionless table and trajectory control. • Development and testing of passive in-line damper. [ABSTRACT FROM AUTHOR]

Local linearization is often used to enable analytical methods in spacecraft dynamics, navigation, and control. However, the linear approximation becomes inaccurate at large distances from the linearization point and/or when the underlying dynamical system is strongly nonlinear. As a result, linearization-based methods like the finite time Lyapunov exponent (FTLE) can underestimate stretching in phase space. Alternatively, this paper presents a semianalytical method to quantify nonlinear stretching: the eigenpairs of higher-order tensors are used to bound the maximum stretching of a state deviation over time. The tenors in question are derived from the Taylor series expansion of a nonlinear solution flow about a reference trajectory, i.e., the state transition tensor (STT) expansion. It is well known that the eigenvalues of the Cauchy–Green tensor (CGT) bound the stretching of state deviations over time for a linear system, and the largest eigenvalue can be related to the FTLE. This paper will present higher-order, nonlinear analogs to the CGT and the FTLE to more accurately bound nonlinear stretching for applications in guidance, navigation, and control. • Linearization is often used to study the time evolution of state deviations. • Linear methods are insufficient for strongly nonlinear systems or large deviations. • Tensor eigenpairs can be used to bound the nonlinear growth of state deviations. [ABSTRACT FROM AUTHOR]

Ground-based full-scale physical experiments on spacecraft have become an essential part of ground simulations. However, achieving a vertical translational degree of freedom for zero-gravity simulation has become a key technological bottleneck for six-degree-of-freedom ground simulations. The combined active–passive vertical zero-gravity system discussed in this paper can achieve zero-gravity simulation in the vertical direction; however, it exhibits deficiencies such as inaccurate modeling, low control precision, and significant control delays. Addressing the issue of inaccurate modeling, this study uses interpretable ODE neural networks to identify the dynamic model of the system. For resolving the problems of poor control precision and significant delays, this study proposes a hybrid control algorithm based on the ODE dynamic model. The controller includes nominal model feedforward, PID feedback, and learning-based feedforward components. Finally, comparative experiments are designed to validate the proposed model-based hybrid control algorithm. Compared to PID-Feedforward controller, the hybrid controller exhibits a higher response speed, while compared to model-based feedforward controller, it exhibits a better control accuracy. Therefore, the proposed hybrid control algorithm based on the ODE dynamic model effectively enhances the control response speed and improves the control precision of the system. • A satellite simulator that realizes vertical zero-gravity simulation by combining active and passive methods. • Higher precision modeling of nonlinear dynamics by interpretable ODE neural networks. • Smaller control error compared with model-based feedforward controller, using model-based hybrid control algorithm. • Faster response speed compared with PID-Feedforward controller, using model-based hybrid control algorithm. [ABSTRACT FROM AUTHOR]

• A TTSS interaction model is established considering the damage of the track slab. • The damaged slab enlarges the vibration of the under-rail structure. • The settlement induces the resonance of the TTSS interaction system. • The mutual interference between settlement and track irregularity is discussed. In this paper, a dynamic model is established to investigate the dynamic behavior of train-track-subgrade-soil (TTSS) interaction. The effects of interfacial damage of the track slab induced by soil settlement on the dynamic interaction system are considered. The model framework is established by the finite element method. The soil settlement-induced track deformation is calculated by a practical iteration algorithm, where the nonlinear interfacial damage is simulated by the cohesive zone model. The simulation model is verified by comparison with other models. In regards to the excitations of the dynamic TTSS interaction system, two types of track irregularities are considered, namely the conventional track irregularities generated by known spectrums, and the additional irregularities caused by soil settlement. In the numerical study, the dynamic performances of the TTSS interaction subjected to interfacial damage, and soil settlement are compared. Next, the short wavelength irregularity is discussed as well. From the results, the vibration enhancement can be observed in the time and frequency domain. The interfacial damage of the track enhances the vibration both in low- and high-frequency domains, while the impacts of settlement are only observed in the frequency band of 0∼3 Hz. The frequency band of vibrations triggered by short wavelength irregularities is correlated with its wavelength range. Moreover, the settlement with different wavelengths and amplitudes is studied. It is shown that the increase of settlement amplitude and decrease of settlement wavelength lead to higher damage degree in amplitude and wider spatial distribution. In regards to the dynamic responses, the vehicle accelerations, wheel-rail contact forces, track displacement, and soil displacement are more sensitive to the settlement amplitudes varying from 10 to 80 mm, while the sensitive settlement wavelength is concentrated in 20 to 40 m. [ABSTRACT FROM AUTHOR]

• Extended Goodwin model integrates endogenous technological change and labor supply. • Reinterpretation of induced innovation in terms of mechanization. • Application of 3D-Hopf bifurcation theorem reveals limit cycle dynamics. • Employment rate's effect on productivity as a bifurcation parameter defines cycle stability. • Numerical simulation for 10 OECD economies and sensitivity analysis. This paper extends the Goodwin model of distributive cycles by incorporating the simultaneous endogeneity of technical change and labor supply within a classical-Marxian framework. It reinterprets induced innovation, suggesting that firms optimize mechanization to maximize cost reduction, obtaining a micro-founded relationship between mechanization and the wage share. Additionally, it assumes a positive relationship between labor supply and the employment rate. The resulting three-dimensional dynamical system includes wage share, employment rate, and capital-output ratio as state variables. The Hopf bifurcation theorem reveals the emergence of limit cycles as the employment rate's effect on labor productivity (reserve-army-creation effect) approximates a critical value from below. Numerical simulations for 10 OECD countries illustrate the cyclical nature of the model and its consistency with empirical patterns. Furthermore, a sensitivity analysis explores the effect of parameters variations, emphasizing the social dimensions of productivity and labor supply as critical factors defining the stability of distributive cycles. [ABSTRACT FROM AUTHOR]

The Goodwin–Keen model was introduced to study the structural instability of debt-financed economies. Despite its theoretical appeal, no empirical study has focused on this model to date. Using u.s. data for non-financial firms over the period 1959–2019, this paper tests the empirical validity of a Goodwin–Keen model accounting for dividends. We propose a two-step procedure to simultaneously estimate parameters and quantify their uncertainty. The model satisfactorily captures the historical cycles in the wage share and employment rate, while reflecting the trend growth in the debt-to-output ratio. The estimation provides meaningful parameters, although their large uncertainty suggests that the model fails to fully account for the private debt dynamics. The estimated model assigns a probability of at most 11% to the occurrence of a private-debt overhang over the 21st century. However, it would have failed to foretell the Global Financial Crisis. Further work is therefore needed to improve its prospective capacity. • A new estimation strategy is used to estimate the parameters of a Goodwin–Keen model for the United-States (1959-2019). • The model captures the historical wage-share, employment rate and corporate debt-to-output ratio trajectories. • The model's behavior is discussed based on prospective simulations and a backtesting over the 2008 crisis period. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the construction of quadratic invariants in a complex phase space under the transformation z = (x + iy) and z ¯ = (x - i y) for various time-dependent systems. For this purpose, Struckmeier and Riedel (SR) approach [ 1, 2 ] is used. The constructed invariants include an unknown function f 2 (t) that is a solution of a third-order differential equation and its coefficients can be determined by the trajectories of the particle. The invariants play an important role in the study of a dynamical system, to access the accuracy in numerical simulations and to investigate the classical and quantum integrability of a system. [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]

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]

In this article, with the help of Matlab R2021a software, the exact solutions of the EW are successfully examined by Sub-Equation method and the unified F-expansion method. The main novelty of this paper lies in the six aspects: (1) Singular periodic wave U-shaped solition is discovered by the sub equation method which did not happen in previous papers [35–37]. (2) More and more intensive multi-periodic M-shape wave solutions are also discovered by the unified F-expansion method which did not happen in previous papers [32,34–37]. (3) The dynamic wave behaviours about the got results and the effects of fractionality α are illustrated by Figs. 1–7. The fractional parameter α masters the appearance of the solitons and makes the involved alphabetic shaped solitions due to the increase in the fractionality number α in Figs. 1–7. (4) The effect about free parameters c , k can be seen from Figs. 8–11 in this paper. If only the increase of wave velocity parameter c or wave number parameter k , the energy trend of the wave is always positive and intensive. This also never happens in previous literatures [34–37]. (5) The Jumarie's modified Riemann–Liouville and beta fractional and conformable derivatives are tested for accuracy in Figs. 12 and 13. We seem firstly compare the relations and distinctions among different fractional order derivatives in EW model. (6) In our best cognitive, the planar dynamical system about EW model whose phase portraits are also first studied. Furthermore, phase portraits for the space–time fractional equal width equation are plotted, and the corresponding sensitivity and chaotic behaviors are analyzed. The geometrical representations of the EW provide the corporal information to explain the physically phenomenons. [ABSTRACT FROM AUTHOR]

Different works in literature have reported that nonlinear controllers based on the energy approach are not effective to completely swing-up an inverted pendulum subjected to friction. Most studies trying to solve this issue consider static friction models in the design of controllers. This consideration is mainly because the stability proof of the system with dynamic friction in closed-loop is difficult. Hence, this paper presents a nonlinear controller with friction compensation to swing-up a Furuta pendulum with dynamic friction. With this aim, we consider that only the active joint of the system is subjected to friction, which is represented via a dynamic model, namely, the Dahl model. We first present Furuta Pendulum dynamic model with dynamic friction. Then, by slightly modifying an energy-based controller that has been previously reported in literature and by including friction compensation, we propose a nonlinear controller that allows to swing-up completely a Furuta pendulum subjected to friction. The unmeasurable friction state is estimated through a nonlinear observer and a stability analysis of the closed-loop system is accomplished with the direct Lyapunov method. Finally, successful experimental results are presented for a Furuta pendulum prototype built by authors. This shows the effectiveness of the proposed controller in achieving a complete swing-up of the Furuta pendulum, in a time feasible for experimental implementation, and ensuring closed-loop stability. [Display omitted] The present paper proposes a nonlinear controller with dynamic friction compensation that experimentally achieves a complete swing-up for the Furuta pendulum in a short time, whose stability analysis is accomplished with the Lyapunov method • A nonlinear control to swing-up a Furuta pendulum with dynamic friction is proposed. • Control is an improved modification of an energy control previously reported. • Modification allows formally demonstrating swing-up accomplishment despite friction. • Three problems by friction in swinging-up inverted pendulums in practice are solved. • Improved performance of the control is successfully verified in practical application. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology to obtain prediction regions of the output of a dynamical system. The proposed approach uses stored past outputs of the system and it is entirely data-based. Only two hyperparameters are necessary to apply the proposed methodology. These scalars are chosen so that the size of the obtained regions is minimized while fulfilling the desired empirical probability in a validation set. In this paper, methods to optimally estimate both hyperparameters are provided. The provided prediction regions are convex and checking if a given point belongs to a computed prediction region amounts to solving a convex optimization problem. Also, approximation methods to build ellipsoidal prediction regions are provided. These approximations are useful when explicit descriptions of the regions are necessary. Finally, some numerical examples and comparisons for the case of a non-linear uncertain kite system are provided to prove the effectiveness of the proposed methodology. • A method to compute prediction regions for multivariate systems is presented. • These regions contain future values of the outputs with a certain probability. • The proposed method does not need any knowledge of the system dynamics. • A procedure to obtain ellipsoidal approximations of the regions is also presented. • The results are illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

• This paper studies the torsional stick-slip vibrations in downhole drilling. • The generalized lumped-parameter model of drill-strings is used. • We analyze the multistability in drill-strings when drilling becomes deeper. • The main features of bifurcation persist under variation of the drill-string length. The generalized lumped-parameter model of the drill-string system is studied in this paper to provide a fundamental understanding of the torsional stick-slip vibrations in downhole drilling. Our investigation focuses on analysing the cause of three coexisting states: bit sticking, stick-slip vibration, and constant rotation. A critical region of multistability is identified based on the lumped-parameter model, and the conditions for switching between these multiple stable states are discussed. Special attention is given to the bifurcation structure of the considered drill-string model, which is obtained via path-following methods for nonsmooth dynamical systems. The bifurcation scenario is compared to the case when a longer drill-string is considered, which amounts to drilling deeper. It is found that the main features of the bifurcation picture persist under variation of the drill-string length, with certain numerical differences regarding for instance the window of multistability. [ABSTRACT FROM AUTHOR]

Electro-hydraulic systems are extensively utilized to generate desired acceleration waveforms to provide a vibration environment for testing the performance and reliability of objects in various industrial applications. However, as electro-hydraulic systems are often affected by some inevitable drawbacks resulted from hydraulic nonlinearities, unwanted dynamic variations and disturbances, the generated acceleration waveform is generally far behind the expectation. In this paper, a convex combined adaptive controller with input shaping technique is proposed for enhancing the transient acceleration waveform replication accuracy of electro-hydraulic systems. The proposed controller is comprised of a three variable controller at the bottom level, an input shaping technique controller at the middle level, and a convex combined adaptive controller at the upper level. The three variable controller is firstly utilized for the establishment of a fundamental closed-loop acceleration control system, and then the input shaping technique controller is constructed by introducing an offline designed inverse prefilter utilizing the multi-innovation recursive least squares algorithm and the zero magnitude error tracking algorithm. The convex combined adaptive controller at the upper level is comprised of two individual adaptive filters with high and low step sizes, which provides the merits of fast convergence rate and high tracking accuracy, and it is further exploited to address for system's dynamic variations, model uncertainties and unexpected perturbations. Comparative experiments of the proposed controller with a manually generated random waveform and a recorded earthquake waveform as the testing inputs are conducted on a typical electro-hydraulic test bench, and the corresponding results demonstrate the feasibility and superiority of the proposed controller in improving the transient acceleration waveform replication performance of electro-hydraulic systems. • A new transient acceleration waveform replication strategy using convex combined adaptive controller with input shaping technique is proposed. • Input shaping technique controller acting as a prefilter is adopted to enhance tracking frequency bandwidth and reduce phase delay error. • Convex combined adaptive controller is exploited to address for system's dynamic variations, model uncertainties and unexpected disturbances. • Experimental results validate feasibility and superiority of the proposed controller than the other comparative methods. [ABSTRACT FROM AUTHOR]

This paper proposes a Repetitive Dynamic Matrix Control (RDMC) for systems with periodic specifications. The new algorithm is able to track periodic references and reject repetitive disturbances with a known period based on a modified prediction error. A repetitive version of the Generalized DMC (GDMC) is also proposed such that it can be applied to control open-loop unstable systems. Only the step-response coefficients are required to describe the dynamical system such that the RDMC preserves the modeling simplicity of the Dynamic Matrix Control (DMC). The proposed solution can be interpreted as an extension of the DMC for repetitive control applications. A data-driven filter design is proposed in order to ensure null prediction steady-state error in the presence of periodic disturbances even for unstable open-loop systems. Two case studies are presented to show the usefulness of the proposed strategy for control systems with periodic specification and to illustrate the typical advantages and drawbacks of the proposed repetitive control extension of the DMC algorithm. • A Repetitive DMC has been proposed for stable and unstable systems. • A new data-driven filter design is presented for unstable systems. • Periodic set-point tracking and repetitive disturbance rejection are achieved. [ABSTRACT FROM AUTHOR]

The Linear Motor-Driven Aerostatic Stage (LMDAS) has been extensively applied in high-precision measuring instruments and precision equipment requiring exceptional velocity and acceleration performance. This is attributable to its low friction, high precision, and high dynamic performance. Nevertheless, the LMDAS is vulnerable to external disturbances due to weak damping of the aerostatic guideway's gas film. This weakness directly affects the positioning accuracy and dynamic characteristics of the system and results in its flutter. This paper proposed a method for improving the overall damping of the system and its ability to suppress vibrations by enhancing the damping of the driving direction via combining active control and passive regulation. The active control algorithm based on the active disturbance rejection controller and the passive regulation technology based on the linear motor were presented, respectively. Both numerical and experimental studies demonstrated that this approach was superior to the traditional PID controller, commonly employed in LMDAS, regarding steady-state performance, dynamic response, and vibration suppression. In particular, this method demonstrated a significant improvement in reducing the maximum vibration acceleration of the LMDAS in all three directions, achieving a 50 % reduction compared to the conventional PID controller. [Display omitted] • Enhancing driving direction's damping to improve the vibration suppression ability. • The method combines active control and passive regulation to enhance damping. • The active controller based on active disturbance rejection controller was developed. • The passive regulation technology of electromagnetic damping was proposed. • Method's effectiveness for improving vibration suppression is verified. [ABSTRACT FROM AUTHOR]

In this paper the bistability of a mathematical model for the control of an olive tree disease is studied. The basin of stability values were computed for three different pairs of bistable equilibrium points by using the software bSTAB. Moreover an extension of the software functionalities is made, first by approximating the shape of the attractors in three dimensions and second by extending the sensitivity study with respect to some important parameters of the numerical scheme, e.g. hyperparameters, to the two dimensional case. Analogously, the bifurcation diagram of the basin of stability values with respect to one parameter of the model was extended to the two dimensional case where two parameters of the model can vary simultaneously. Finally an approximation of the surfaces of the sensitivity analysis and bifurcation diagrams were made. [ABSTRACT FROM AUTHOR]

The dynamical behavior of the Lakshamanan-Porsezian-Daniel (LPD) model with applications in nonlinear optics is uncovered in this paper. The incorporation of spatio-temporal dispersion into the model, addressing the internet bottleneck issue, is emphasized. A planar dynamical system (DS) is accounted for by applying the Galilean transformation to the considered model. All types of phase portraits are plotted based on specific values of parameters. For the generation of quasi-periodic and chaotic patterns, A cos ⁡ (Ω τ) with strength and frequency components is added. The resulting quasi-periodic and chaotic orbits are also plotted. Various bifurcation and chaos detecting tools, such as time series analysis, Poincare maps, Lyapunov exponent, bifurcation diagrams, and sensitivity, are employed to examine the behavior of the obtained dynamical system under proposed initial conditions. The Hamiltonian function is calculated and plotted for the unperturbed dynamical system. Multi-stability phenomena demonstrate the coexistence of multi-stable orbits in their dynamic features. The dynamics of pulse propagation are found to be significantly impacted by the spatio-temporal dispersion. [ABSTRACT FROM AUTHOR]

The paper discusses the dissipative control problem of nonlinear singularly perturbed systems (SPSs) with dynamic quantization and actuator failure. The nonlinear singularly perturbed plant is described by Takagi–Sugeno (T–S) fuzzy model. The dynamic quantizer is considered to realize the effective utilization of the limited network channel bandwidth resources, and the possible transmission failure between the controller and the actuator is also considered. Based on linear matrix inequalities, sufficient design conditions for the ϵ -independent state feedback controller are given such that the constructed quantized closed-loop system is asymptotically stable and satisfies a predefined dissipative performance. Furthermore, a short search algorithm is given to search the maximum stability bound ϵ ̄. Finally, two examples are provided in order to prove the feasibility and effectiveness of the proposed method. • A state feedback control scheme is proposed for fuzzy singularly perturbed systems. • The dissipative performance of fuzzy singularly perturbed systems is analyzed. • Sufficient conditions are given to design the controller and the quantizer. [ABSTRACT FROM AUTHOR]

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions. [ABSTRACT FROM AUTHOR]

This paper aims to present an analytical as well as a comparative study to investigate the effect of the Brinkman porous medium on the onset of regular and chaotic motion in cylindrical enclosures of different heights. The hybrid bi-viscous Bingham nanoliquid is considered as the working fluid. Modified Brinkman–Buongiorno and bi-viscous Bingham fluid models are incorporated to obtain the flow governing dynamics. The thermophysical properties of the hybrid nanoliquid are calculated using phenomenological laws and the mixture theory. The study is carried out for the axisymmetric mode, and the Bessel functions are taken as the eigenfunctions of the problem. Double Fourier–Bessel series expansions are used for weakly non-linear stability analysis. The limiting cases of the study are obtained, and the results on the onset of convection, heat, and mass transport are discussed graphically. The behavior of the dynamical system is analyzed using the maximum Lyapunov exponent plot, the bifurcation diagram, and phase plots. Outcomes suggest that convection sets in earlier in the water-based hybrid nanoliquid than in the bi-viscous Bingham hybrid nanoliquid. The use of Single-walled carbon nanotubes enhances the heat transfer rate by approximately 17%. Further, it is concluded that a tall cylindrical enclosure is the most favorable geometry for achieving a higher heat transfer rate among the others. [ABSTRACT FROM AUTHOR]

The launcher recovery method known as 'In-Air Capturing' is an innovative approach where a winged rocket stage is captured mid-air by an aircraft and subsequently towed back to the launch site. To achieve this, a capturing device attached to a tether is released from the towing aircraft. This device autonomously connects the reusable launch vehicle to the aircraft, while the two vehicles are in proximity. The tether's flexible dynamics have a strong influence on the maneuverability of the capturing device. Thus, it is critical to model the dynamics of the tether to get a realistic understanding and to evaluate feasibility of the concept. However, precise modelling and control of highly flexible systems with large deformations is both challenging and computationally intensive. For engineering applications which involve closed-loop simulations, finding a trade-off between accuracy and computational effort is crucial. In this paper, the tether is modelled as a discretized chain of rigid bodies connected by rotational springs at the joints. The tether along with the capture system is integrated in a simulation model and open loop tests are performed to analyse the system characteristics. The tether properties are studied to find a suited configuration for 'In-Air Capturing'. • Multibody modelling approach for long cable like bodies with large deformation. • Capture system dynamics for the unique 'In-Air Capturing' launcher recovery concept. • Dynamic modelling for the complete capturing system including towing aircraft, capturing device and tether. • Assessment of tether properties suited for 'In-Air Capturing' with sensitivity studies. [ABSTRACT FROM AUTHOR]

Solar photovoltaic systems can reduce carbon emissions by harnessing green energy from the sunlight, however, tremendous end-of-life solar panels may pose a threat to the local environment in the coming decades. What's worse, fewer regulations have been mandated to deal with the disposal of solar waste. To address this issue, this paper investigates a game-based, government-subsidized solar recycling model, and extends the model to a dynamic system. By analyzing the equilibrium outcomes, optimal decisions are revealed for all stakeholders. More importantly, we find regulatory subsidies can benefit all members of the solar recycling chain. Furthermore, when confronted with low-quality solar panels with a high degradation rate, we suggest that the government announces a low R&D subsidy rate. Even so, the level of the manufacturer's R&D efforts is still high, which leads to more R&D subsidies provided by the government. Based on an analysis of the dynamic system, it's better to be extremely careful when the government enacts the subsidy policy. Otherwise, the profits of all the chain members may be hurt due to the bifurcation and chaos phenomena. • A government-subsidized solar recycling model has been studied. • The impacts of subsidy and risk aversion on optimal strategies are revealed. • When facing low-quality panels with a high degradation rate, the governor should provide a low R&D subsidy rate. • A dynamic system is investigated to understand decision making process in long-term operations. [ABSTRACT FROM AUTHOR]

The main problem addressed in this paper is the task-space bipartite formation tracking problem of uncertain heterogeneous Euler–Lagrange systems in predefined time. To solve this problem, an effective hierarchical predefined-time control algorithm is designed. This algorithm utilizes a non-singular sliding surface, allowing for the adjustment of the upper bound of the settling time as a flexible parameter. Key components of the proposed approach include an estimator for the leader's states and a controller tailored to the formation problem. To mitigate the effects of dynamic uncertainties in the system, the radial basis function neural network is integrated into the methodology. Finally, the effectiveness and validity of the proposed algorithm are demonstrated through numerical simulations, showcasing their practical applicability and efficacy. • Novel sliding mode control strategy tackles the bipartite formation problem. • The task-space controller considers the agents with different degrees-of-freedoms. • Neural network addresses the lumped uncertainties of the dynamic models. • Estimation and tracking errors converge to the origin in a predefined time. [ABSTRACT FROM AUTHOR]

This paper explores the design of a positive l 1 -gain asynchronous non-fragile fault detection filter (FDF) for discrete-time positive Markov jump systems (PMJSs) based on the dynamic event-triggered method (DETM). Due to the effect of positivity on event-triggered mechanisms and non-triviality on stability of discrete-time PMJSs, a new more powerful and generic DETM that can avoid non-triviality is developed. The asynchronous situation between the non-fragile FDF modes and the system modes is effectively managed by employing a hidden Markov model. Then, the solvability criteria for issues of concern are presented by building the copositive Lyapunov function (CLF) with internal dynamic variables (IDV). An alternative sufficient condition is derived based on the obtained results. Subsequently, a co-design project of the expected dynamic event-triggered positive l 1 -gain asynchronous non-fragile fault detection filter (DETPGAN-FFDF) and the designed DETM is proposed in this paper. Finally, the effectiveness and superiority of the approach are verified by numerical arithmetic examples and practical applications based on pest management. • In terms of positivity, an LP form of DETM for discrete-time PMJS is developed, which may further reduce data transmission and eliminate non-triviality. Besides, the DETM proposed in the paper covers the static event-triggered method (SETM), which is more versatile. • Considering the asynchrony between PMJSs and FDF, the HMM is introduced to address this dilemma effectively. • By constructing the copositive Lyapunov function with internal dynamic variables, a stability criterion is derived to guarantee that the augmented system is positive and stochastically stable with l1-gain performance. Based on the obtained criterion, we give another sufficient condition. • The required co-design scheme between DETPGAN-FFDF and DETM proposed in this paper is implemented, where the design of the non-fragile FDF eliminates the potential impact of faults or fluctuations on the FDF's performances. In addition, the merits of the proposed DETM and its influence on fault detection are analyzed in detail with numerical examples. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel fractional-order hyperchaotic system is investigated. • Existence of chaotic attractors just in the fractional-order case, in this system, are reported. • Bifurcation diagrams and corresponding Lyapunov spectrum are computed. • The work reports the first example that shows existence of chaotic attractors that exist only in fractional-order case. Studying chaotic dynamics in fractional- and integer-order dynamical systems has let researchers understand and predict the mechanisms of related non-linear phenomena. Phase transitions between the fractional- and integer-order cases is one of the main problems that have been extensively examined by scientists, economists, and engineers. This paper reports the existence of chaotic attractors that exist only in the fractional-order case when using the specific selection of parameter values in a new hyperchaotic (Matouk's) system. This paper discusses stability analysis of the steady-state solutions, existence of hidden chaotic attractors and self-excited chaotic attractors. The results are supported by computing basin sets of attractions, bifurcation diagrams and the Lyapunov exponent spectrum. These tools verify the existence of chaotic dynamics in the fractional-order case; however, the corresponding integer-order counterpart exhibits quasi-periodic dynamics when using the same choice of initial conditions and parameter set. Projective synchronization via non-linear controllers is also achieved between drive and response states of the hidden chaotic attractors of the fractional Matouk's system. Dynamical analysis and computer simulation results verify that the chaotic attractors exist only in the fractional-order case when using the specific selection of parameter values in the Matouk's hyperchaotic system. An example of the existence of hidden and self-excited chaotic attractors that appears only in the fractional-order case is discussed. So, the obtained results give the first example that shows chaotic states are not necessarily transmitted between fractional- and integer-order dynamical systems when using a specific selection of parameter values. Chaos synchronization using the hidden attractors' manifolds provides new challenges in chaos-based applications to technology and industrial fields. [ABSTRACT FROM AUTHOR]

Gaussian Mixture Models and State Transition Tensors are combined to propagate state uncertainty to demonstrate an analytical and accurate future uncertainty and conjunction assessment. The initial uncertainty distribution is split into a Gaussian Mixture Model to reduce the size of covariance associated with each mixture component. This reduction in size allows for a significantly more accurate nonlinear mapping of each individual component. For higher accuracy in the mixture component propagation, State Transition Tensors are used to capture the nonlinear effects due to higher-order dynamics, as shown already in work by Fujimoto and Scheeres. In this paper, this GMM-STT method is used to analyze collisions using different dynamical models. The first case study demonstrates the application of this method in two-body problem dynamics; the second also adds J 2 secular effects; and the third brings in full J 2 and Solar Radiation Pressure dynamics through a Simplified Dynamical System. This paper also includes a two-body problem repeating conjunction example to establish a relationship between the propagation time and the number of mixture components needed for an accurate probability of collision computation. In each example, as the number of mixture components increases, the probability of collision converges with the Monte Carlo truth, proving the feasibility of this method. • Orbit Determination models make accurate uncertainty propagation essential. • Propagation with nonlinear dynamics leads to non-Gaussian future uncertainty. • Conjunction models require accurately propagated future state and uncertainty. • Gaussian Mixture Model - State Transition Tensor model gives accurate uncertainty. • Model accuracy is confirmed with comparison to Monte Carlo Probability of Collision. [ABSTRACT FROM AUTHOR]

In this paper, based on the sampled-data observer and the deterministic learning theory, a rapid dynamical pattern recognition approach is proposed for univariate time series composed of the output signals of the dynamical systems. Specifically, locally-accurate identification of inherent dynamics of univariate time series is first achieved by using the sampled-data observer and the radial basis function (RBF) networks. The dynamical estimators embedded with the learned knowledge are then designed by resorting to the sampled-data observer. It is proved that generated estimator residuals can reflect the difference between the system dynamics of the training and test univariate time series. Finally, a recognition decision-making scheme is proposed based on the residual norms of the dynamical estimators. Through rigorous analysis, recognition conditions are given to guarantee the accurate recognition of the dynamical pattern of the test univariate time series. The significance of this paper lies in that the difficult problems of dynamical modeling and rapid recognition for univariate time series are solved by incorporating the sampled-data observer design and the deterministic learning theory. The effectiveness of the proposed approach is confirmed by a numerical example and compressor stall warning experiments. • An observer-based recognition approach is proposed for univariate time series. • The challenge of learning dynamical systems from univariate time series is overcome. • Estimators perform recognition tasks, reducing computational complexity. • Average residual norms are used for decisions, which ensures recognition accuracy. [ABSTRACT FROM AUTHOR]

• The negative stiffness inertial amplifier tuned mass dampers is introduced. • The new closed-form expressions for optimal design parameters of NSIA-TMDs. • The H 2 and H ∞ optimization based closed-form expressions for optimal design parameters. • NSIA-TMDs shows 50% better vibration reduction capacity than conventional TMD. The negative stiffness inertial amplifier tuned mass dampers (NSIA-TMD) are introduced in this paper. Another two novel tuned mass dampers such as negative stiffness tuned mass damper (NS-TMD) and inertial amplifier tuned mass damper (IA-TMD) are mathematically developed from the negative stiffness inertial amplifier tuned mass dampers (NSIA-TMD) and the static masses of these three novel dampers are retained constant. The exact closed-form expressions for optimized system parameters for these novel dampers are obtained using H 2 and H ∞ optimization techniques. The dynamic responses of the SDOF systems controlled by H 2 and H ∞ optimized novel tuned mass dampers subjected to base excitations are obtained analytically. The dynamic response reduction capacities of the novel tuned mass dampers are compared with the dynamic response reduction capacities of traditional tuned mass dampers (TMD). Therefore, the dynamic response reduction capacities of H 2 optimized NS-TMD, NSIA-TMD, and IA-TMD are significantly 45.51 % , 43.47 % , 41.08 % superior to the H 2 optimized traditional tuned mass dampers. Furthermore, the dynamic response reduction capacities of H ∞ optimized NS-TMD, NSIA-TMD, and IA-TMD are significantly 3.31 % , 8.98 % , 13.79 % superior to the H ∞ optimized traditional tuned mass dampers. The nonlinear negative stiffness inertial amplifier tuned mass dampers (NNSIA-TMD) are also introduced in this paper. As a result, the dynamic response reduction capacities of H 2 optimized nonlinear negative stiffness tuned mass damper (NNS-TMD), NNSIA-TMD, and nonlinear inertial amplifier tuned mass damper (NIA-TMD) are significantly 24.54 % , 21.92 % , 19.12 % superior to the H 2 optimized traditional tuned mass dampers. Furthermore, the dynamic response reduction capacities of H ∞ optimized NNS-TMD, NNSIA-TMD, and NIA-TMD are significantly 3.01 % , 9.04 % , 15.08 % superior to the H ∞ optimized traditional tuned mass dampers. The outcomes of this research are mathematically accurate and relevant to practical design applications. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a generalization of Schrödinger operator, known as Hamiltonian with finite range. We prove the related Gordon's lemma with quantitative conditions which means the absence of point spectrum. [ABSTRACT FROM AUTHOR]