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We study a system of ordinary differential equations in R5 that is used as a model both in population dynamics and in game theory and is known to exhibit a heteroclinic network consisting in the union of four types of elementary heteroclinic cycles. We show the asymptotic stability of the network for parameter values in a range compatible with both population and game dynamics. We obtain estimates of the relative attractiveness of each one of the cycles by computing their stability indices. For the parameter values ensuring the asymptotic stability of the network we relate the attractiveness properties of each cycle to the others. In particular, for three of the cycles we show that if one of them has a weak form of attractiveness, then the other two are completely unstable. We also show the existence of an open region in parameter space where all four cycles are completely unstable and the network is asymptotically stable, giving rise to intricate dynamics that has been observed numerically by other authors. [ABSTRACT FROM AUTHOR]

To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cycles represent coexisting species. The stability of all heteroclinic cycles in the network for the Jungle Game with four species determines that only three species coexist in the long-run, interacting under cyclic dominance as a Rock–Paper–Scissors Game. This is in stark contrast with other interactions involving four species, such as cyclic interaction and intraguild predation. We use the Jungle Game with four species to determine the success of a fourth species invading a population of Rock–Paper–Scissors players. [ABSTRACT FROM AUTHOR]

This paper investigates the Cauchy problem for time‐space fractional Keller‐Segel‐Navier‐Stokes model in ℝd(d≥2)$$ {\mathrm{\mathbb{R}}}^d\kern0.1em \left(d\ge 2\right) $$, which can describe the memory effect and anomalous diffusion of the considered system. The local and global existence and uniqueness in weak Lp$$ {L}^p $$ space are obtained by means of abstract fixed point theorem. Moreover, we explore the asymptotic stability of solutions as time goes to infinity. [ABSTRACT FROM AUTHOR]

In this paper, a viscous shock wave under space-periodic perturbation of 1-D isentropic Navier-Stokes system in the half space is investigated. It is shown that if the initial periodic perturbation around the viscous shock wave is small, then the solution time asymptotically tends to a viscous shock wave with a shift partially determined by the periodic oscillations. Moreover the strength of shock wave could be arbitrarily large. This result essentially improves the previous work Matsumura and Mei (1999) [14] where the strength of shock satisfies some restrictions and the initial periodic oscillations vanish. [ABSTRACT FROM AUTHOR]

This paper presents various bifurcations of the McMillan map under perturbations of its coefficients, such as period-doubling, pitchfork, and hysteresis bifurcation. The associated existence regions are located. Using the quasi-Lyapunov function method, the existence of asymptotically stable fixed point is also demonstrated. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stable economic model predictive control (EMPC) strategy for constrained nonlinear systems with changing economic criteria. The traditional EMPC may lead to infeasibility and even instability of the closed-loop system when the criterion has been changed. Firstly, a generalised terminal constraint is introduced to ensure the recursive feasibility of the economic optimisation problem, which enforces the terminal states to converge to an arbitrary equilibrium state rather than a predetermined fixed one at the initial time. Then the stability constraint is constructed by solving an auxiliary optimisation problem online, which is the key to guaranteeing the asymptotic stability of the closed-loop system. Finally, sufficient conditions for feasibility and asymptotic stability are derived in the context of changing economic criteria. The main feature of the proposed strategy is that it does not need to know the changes of economic criterion in advance, and its properties and effectiveness are exemplified by simulations on a nonlinear chemical process example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. [ABSTRACT FROM AUTHOR]

In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on R × T L and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag (SIAM J Math Anal 44:1175–1210, 2012). Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod (Ann Inst H Poincaré Anal Non Lineaire 32:347–371, 2015) and modifying the mobile distance in Nakanishi and Schlag (2012), we construct a contraction map on the graph space. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results. [ABSTRACT FROM AUTHOR]

Atherosclerosis, as a chronic inflammatory disease, has been a threat to human health. How to diagnose and prevent this disease has long been the focus of medical and biomathematics study. In this paper, we investigate a free boundary model of an atherosclerotic plaque formation in the presence of reverse cholesterol transport, which includes low-density lipoprotein, high-density lipoprotein, endothelial stimulating cytokines, pro-inflammatory and anti-inflammatory macrophages, as well as foam cells. For this model, we use the Holling type-III response function instead of the usual Holling type-II to describe the change of the concentration of each substance. We first introduce the auxiliary function ξ (r) to prove the existence and uniqueness of small radially symmetric stationary plaque for appropriate L 0 and H 0 by using the contraction mapping principle and maximum principle, and then establish a condition to ensure their asymptotic stability behavior by expanding the corresponding steady-state solution. [ABSTRACT FROM AUTHOR]

This article investigates the asymptotic stability of fractional-order (FO) systems with uncertainty and time-varying delay based on the sliding mode control (SMC) method. First, based on the SMC method, a suitable integral type fractional-order sliding mode surface (FOSMS) is designed and the dynamic equations of FO systems under SMC are obtained. Second, by inequality techniques, the condition for asymptotic stability of the FO system has been mathematically established. Then, a novel adaptive SMC law is introduced, which can make sure the accessibility of sliding mode surfaces (SMS). Finally, the feasibility of the results obtained in this paper is verified through a simulation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this short note we indicate some improvement of an article published in this journal by Crespo, Ivorra and Ramos 6. The techniques used are connected with several smoothing effects associated with linear partial differential operators which give rise to some accretive operators in L¹(Ω), as well as with some H²(Ω) estimates independent on time. [ABSTRACT FROM AUTHOR]

Abstract: We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model. [Copyright &y& Elsevier]

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper. [ABSTRACT FROM AUTHOR]

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov–Kuznetsov equation in dimensions two and three. We also derive a qualitative version of the orbital stability result, which will be useful for studying the collision of two solitary waves in a forthcoming paper. The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by Côte, Muñoz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three. [ABSTRACT FROM AUTHOR]

The stabilization problem for uncertain discrete‐time singular Markovian jump systems (DSMJSs) with time‐varying delays is comprehensively covered in this paper. An updated Lyapunov–Krasovskii functional is presented via a discrete state decomposition method. With the help of this constructed Lyapunov–Krasovskii functional, some delay‐ and mode‐dependent sufficient conditions for the open‐loop DSMJSs are derived. Based on these circumstances, a memory mode‐dependent state feedback control is used to create a closed‐loop DSMJS with parameter uncertainties that is regular and causal. And then, the stochastically admissible conditions are attained. Through the exact calculation of each decomposition component for the designed memory state feedback controller, the intended memory state feedback controller settings are determined. It should be mentioned that the algorithm suggested in this article expands the controller design's feasibility and flexibility. The numerical results show how the approach is superior to previous ones, and the given results are less conservative. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals which are called event times. Sufficient conditions are established to guarantee asymptotic stability of the resulting impulsive systems. It is worth mentioning that the event times are different from the impulse times, that is, the control signals are updated at each event time but the actuator performs the impulsive control tasks at a later time due to time delays. The effectiveness of our theoretical result with the proposed scheme is illustrated by three examples. [ABSTRACT FROM AUTHOR]

In this paper, the optimal formation control issue with collision avoidance and connectivity assurance is investigated for a class of second-order uncertain nonlinear multi-agent systems. First, the neural networks are employed in order to deal with the unknown nonlinear dynamics of the system. Then, an optimal formation control scheme is developed in the framework of the identifier–actor–critic. By constructing a new performance metric function containing collision avoidance and connectivity constraints, it is demonstrated that asymptotic convergence of the tracking error can be achieved under the proposed control scheme. Finally, the effectiveness of the proposed control method is validated by the numerical simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing secure control for networked multi-agent systems (MASs) under Denial-of-Service (DoS) attacks. We propose a constructive design method based on the interaction topology. The MAS with a non-attack communication topology, modeled by quasi-Abelian Cayley graphs subject to DoS attacks, can be represented as a switched system. Using switching theory, we provide easily implementable sufficient conditions for the networked MAS to remain asymptotically stable despite DoS attacks. Our results are applicable to both continuous-time and discrete-time systems, as well as to discrete-time systems with variable steps or systems that combine discrete and continuous times. [ABSTRACT FROM AUTHOR]

In many smart systems, such as cloud computing, networked control, manufacturing, and telecommunication, the effects of time delays are unavoidable. Saturation nonlinearity is common in many smart systems (e.g. electric systems with limited actuator power supplies, mechanical systems with position and speed constraints, fixed-point digital filters, etc.). Therefore, the study of stability of discrete-time systems (DTSs) with time delay and saturation is of high importance in practice. The global asymptotic stability (GAS) problem of such systems is investigated in this paper. The saturation nonlinearity is constrained by a convex hull with a free matrix whose infinity norm is smaller than or equal to unity. A new Lyapunov-based GAS criterion for DTSs with time-varying delay and state saturation is established. The GAS problem for DTSs with constant delay and saturation is also discussed. The obtained results can be used to ensure the absence of overflow oscillations in the considered system. In comparison to several existing criteria, the approach yields improved stability results. An example is provided to demonstrate the importance of the presented results. [ABSTRACT FROM AUTHOR]

This paper deals with the integration of input move-blocking into the framework of suboptimal model predictive control. The blocked input parameterisation is explicitly considered as a source of suboptimality. A straightforward integration approach is to hold back a manually generated stabilising fallback solution in some buffer for the case that the optimiser does not find a better input move-blocked solution. An extended approach superimposes the manually generated stabilising warm-start by the move-blocked control sequence and enables a stepwise improvement of the control performance. In addition, this contribution provides a detailed review of the literature on input move-blocked model predictive control and combines important results with the findings of suboptimal model predictive control. A numerical example supports the theoretical results and shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• We consider a new type of the Brownian motion: stochastic mass. • We use Markovian jump to describe the discrete nature of the variable mass. • The mass perturbation has a greater effect on the stability of the system than stochastic external excitation. Stochastic mass has exerted a profound impact on the dynamics of the systems characterized by light mass and compact volume. This work delves into the asymptotic stability with probability one of a variable mass energy harvester. Firstly, the Gaussian white noise with Markovian jump is coupled to model the inherent randomness and discreteness of stochastic mass. Then, we have established an approximate dimensionless system based on an equivalent transformation. Using the stochastic averaging method, the averaged Itô stochastic differential equation of the amplitude within the approximated system is derived. With the linearization, we have deduced the largest Lyapunov exponent for the linearized equation. Furthermore, the necessary and sufficient condition for achieving asymptotic stability of the nonlinear energy harvester is proposed approximately by managing the largest Lyapunov exponent be negative. The study systematically dissects the effects of stochastic mass and Markovian jump on the asymptotic stability with probability one of a nonlinear energy harvester. Under the disturbance of stochastic mass, with the increase of linear stiffness, the stability of the system will change nonlinearly. Moreover, the stability regions of the nonlinear energy harvester under varying transition matrices and stochastic mass noise intensities are thoroughly given. The findings and conclusions presented in this paper have a certain theoretical significance for the management of the system stability in engineering practical. [ABSTRACT FROM AUTHOR]

Distribution-dependent stochastic differential equations (DDSDEs, in short), also called as McKean–Vlasov SDEs, are a special class of SDEs and have some concrete applications in mean-field control, mean-field games and complex networks. Stability plays fundamental role among the theory and applications for DDSDEs. In this paper, we discuss a class of distribution-dependent stochastic differential equations driven by time-changed Brownian motions (TDDSDEs, in short). The main aim of this paper is to establish the stability for TDDSDEs. Sufficient conditions are provided to guarantee the solutions to be stable in different senses with regard to a part of the variables in terms of a Lyapunov function. Two examples are given to show the usefulness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Designing a reasonable M/G/1 retrial queue system that enhances service efficiency and reduces energy consumption is a challenging issue in Information and Communication Technology systems. This paper presents an M/G/1 retrial queue system incorporating random working vacation (RWV) and improved service efficiency during vacation (ISEV) policies, and examines its optimal queuing strategies. The RWV policy suggests that the server takes random working vacations during reserved idle periods, effectively reducing energy consumption. In contrast, the ISEV policy strives to augment service efficiency during regular working periods by updating, inspecting or maintaining the server on vacations. The system is transformed into a Cauchy problem to investigate its well-posedness and stability, employing operator semigroup theory. Based on the system's stability, steady-state performance measures, such as service efficiency, energy consumption and expected costs, are quantified using the steady-state solution. The paper subsequently demonstrates the existence of optimal queuing strategies that achieve maximum efficiency and minimum expected costs. Finally, two numerical experiments are provided to illustrate the effectiveness of the system. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of solutions for a new class of generalized Halanay inequalities is studied via the fixed point method. This research provides a new approach to the study of the stability of Halanay inequality. To make the application of fixed point method in stability research more flexible and feasible, we introduce corresponding functions to construct an operator according to different characteristics of coefficients. The results obtained in this paper are applied to the stability study of a neural network system, which has high value in application. Moreover, three examples and simulations are given to illustrate the results. The conclusions in this paper greatly improve and generalize the relative results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we study collective decision‐making in a multi‐population framework, where groups of individuals represent whole populations that interact by means of a regular network. Each group consists of a number of players and every player can choose between two options. A group is characterized by three variables, the first two denoting the fractions of individuals committed to each option and the last one representing the fraction of players not committed to either option. The state of every population is influenced by the state of neighboring groups. The contribution of this work is the following. First, we find explicit expressions for all the equilibrium points of the proposed system, and show that these represent equilibrium points where populations reach consensus, namely, where all populations have the same states. We also derive a sufficient condition for local asymptotic stability as well as exponential asymptotic stability. Then, we study a structured model where every population is now assumed to represent a structured complex network. We conclude the paper by providing a set of simulations that corroborate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study the positive solution to a k-order rational fuzzy difference equation with the form an+1 = 1+ an/ T + an-k, n ∈ N, here, {an} is a sequence of positive fuzzy numbers, T ∈ R+f (positive fuzzy numbers) and the initial values a-t ∈ R+ f (t = 0; 1; · · · ; k); k ∈ N. The focus of this paper is to analyze the dynamic behavior of this fuzzy difference equation. Furthermore, numerical example emphasize the validity of theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we study the asymptotic stability problem for KdV solitons on the half-line, with zero boundary condition and absence of the drift term, represented as ux. Unlike standard KdV, these are not exact solutions to the equation. In a previous result, we showed that these solitons are orbitally stable, provided they are placed sufficiently far from the origin. In this paper, we prove their asymptotic stability in the energy space, and provide decay properties for all remaining regions, except the "small soliton region". For the proof we follow the ideas by Martel and Merle for the big soliton part, and for the linearly dominated region we follow recent results on generalized KdV decay [C. Muñoz and G. Ponce, Comm. Math. Phys., 367 (2019), pp. 581-598, A. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers certain neutral differential equation with the distributed delayWithout imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355–361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result. [Copyright &y& Elsevier]

This paper is concerned with quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Its main theorem establishes global-in-time existence and asymptotic stability of strong solutions to the Cauchy problem close to homogeneous reference states in d ≥ 3 space dimensions. Notably, the operators are not required to be symmetric hyperbolic, instead merely the existence of symbolic symmetrizers is assumed. The dissipation is characterized by algebraic conditions implying the uniform decay of all Fourier modes at the reference state. On a technical level, the theory developed herein uses para-differential operators as its main tool. Apparently being the first to apply such operators in the context of global-in-time existence of small solutions for quasi-linear hyperbolic systems, the present work contains a new version of the strong Gårding inequality. In the context of theoretical physics, the theorem applies to recent formulations for the relativistic dynamics of viscous, heat-conductive fluids such as notably that of Bemfica, Disconzi and Noronha (2018) [2]. [ABSTRACT FROM AUTHOR]

In this paper, the existence and uniqueness of almost automorphic solutions in distribution to McKean–Vlasov stochastic differential equations are established provided the coeffcients satisfy some suitable conditions. The asymptotic stability of the unique almost automorphic distribution solution is discussed in the square-mean sense. Finally, some examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper presents an advanced control strategy based on Fractional-Order Sliding Mode Control (FO-SMC), which introduces a robust solution to significantly improve the reliability of robotic manipulator systems and increase its control performance. The proposed FO-SMC strategy includes a two-key term-based Fractional Sliding Function (FSF) that presents the main contribution of this work. Additionally, a fractional-order-based Lyapunov stability analysis is developed for a class of nonlinear systems to guarantee the asymptotic stability of the closed loop system. Four FSF-based versions of the designed FO-SMC are studied and discussed. Various scenarios of the proposed control strategy are tested on a 3-degree-of-freedom SCARA robotic arm and compared to recent FO-SMC works, demonstrating the effectiveness of the new proposed control strategy to (i) ensure the asymptotic stability, (ii) achieve a smooth start-up, (iii) cancel the static error, giving a good tracking trajectory, and (iv) reduce the control torques, yielding a consumed energy minimization. [ABSTRACT FROM AUTHOR]

To address the nonlinear stabilization problem and improve the tracking control feature of ball on plate system (BPS), this paper puts forward a novel Takagi Sugeno (TS) fuzzy control augmented with the current cycle feedback iterative learning control (CCF-ILC) scheme. According to Bode's sensitivity integral, the performance of linear controllers is always a trade-off between reference tracking and robustness. Hence, to deal with the so-called 'waterbed' effect, this work exploits the capability of TS fuzzy to handle the nonlinear dynamics and synthesizes a learning control scheme based on current iteration error to capitalize the information rich error signal for enhancing the robustness and trajectory tracking features. The global asymptotic stability of the proposed TS fuzzy augmented ILC scheme is proved using the Lyapunov function and linear matrix inequalities (LMIs). Moreover, the monotonic convergence of ILC is presented based on the singular value condition. For identifying the rolling mass from the video stream, a background subtraction algorithm based on thresholding technique is implemented. Finally, the robustness and tracking features of the proposed scheme are evaluated on a two degrees of freedom (DoF) laboratory scale BPS system through hardware in loop (HIL) testing for three realistic test cases. The tracking performance quantified using the root mean square error (RMSE) and power spectral density plot corroborates that the proposed scheme can offer better setpoint tracking and robustness feature compared to state-of-the-art fuzzy and ILC control techniques implemented on BPS. [ABSTRACT FROM AUTHOR]

This paper investigates the stability behaviour of externally interfered discrete-time system under the influence of various finite-register length nonlinearities. Such nonlinearities include quantization and overflow which are commonly originated during hardware implementation. The proposed criteria guarantee the realization of limit-cycle free discrete-time system in the presence of external disturbances and finite-register length nonlinearities. The stability conditions are fabricated by employing passivity-based approach under combinations of quantization and overflow nonlinearities. With the help of the appropriate Lyapunov function along with the passivity condition, the asymptotic stability for the discrete-time system is also ensured under zero disturbance. Relevant examples are presented to show the applicational scope of the work. [ABSTRACT FROM AUTHOR]

Attitude control of a satellite with three flexible elements is considered. Control torque is developed by a set of reaction wheels, which are installed on the central hub of the satellite. The flexible elements are large, so the control torque constraints must be taken into account. In the paper, a control algorithm based on a linear-quadratic regulator is studied. The asymptotic stability of this control is shown. The choice of the control parameters is based on the closed form solution of the corresponding algebraic Riccati equation, which is supplemented by the linear matrix inequality. To increase the convergence rate, particle swarm optimization is used to tune the control parameters. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of solutions to a Ladyzhenskaya fluid model with unbounded variable delay. We first prove the existence, uniqueness and regularity of global weak solutions to the Ladyzhenskaya model by using Galerkin approximations and the energy method based on some suitable assumptions about external forces. Then we obtain that the stationary solution is locally stable. Finally, we establish that the stationary solution has polynomial stability in a particular case of unbounded variable delay. [ABSTRACT FROM AUTHOR]

This paper studied the incompressible Navier-Stokes (NS) equations with nonlocal diffusion on T d (d ≥ 2). Driven by a time quasi-periodic force, the existence of time quasi-periodic solutions in the Sobolev space was established. The proof was based on the decomposition of the unknowns into the spatial average part and spatial oscillating one. The former were sought under the Diophantine non-resonance assumption, and the latter by the contraction mapping principle. Moreover, by constructing suitable time weighted function space and using the Banach fixed point theorem, the asymptotic stability of quasi-periodic solutions and the exponential decay of perturbation were proved. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic stability of fractional-order neural networks (FONNs) with time delay utilizing a sampled-data controller. Firstly, a novel class of Lyapunov–Krasovskii functions (LKFs) is established, in which time delay and fractional-order information are fully taken into account. Secondly, by combining with the fractional-order Leibniz–Newton formula, LKFs, and other analysis techniques, some less conservative stability criteria that depend on time delay and fractional-order information are given in terms of linear matrix inequalities (LMIs). In the meantime, the sampled-data controller gain is developed under a larger sampling interval. Last, the proposed criteria are shown to be valid and less conservative than the existing ones using three numerical examples. [ABSTRACT FROM AUTHOR]

This paper analyses the stability of cycles within a heteroclinic network formed by six cycles lying in a three-dimensional manifold, for a one-parameter model developed in the context of polymatrix replicator equations. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so-called projective map. The stability of the fixed points of the projective map determines the stability of the associated cycles. The description of this new asymptotic approach is applicable to more general types of networks and is potentially useful in computational dynamics. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the influence of time delay effect and steady flow control strategy on traffic flow. Consider that the time delay in sensing flux information during the operation of traffic system is inevitable. Meanwhile, a new method is applied to model and analyse traffic system. A novel discrete‐time lattice hydrodynamic model considering time delay is introduced in this paper. Based on the proposed model with constant and varying time‐delay, the asymptotic stabilities are investigated and corresponding stable conditions are derived. The traffic flow evolution trend with and without time delay is conducted and compared by numerical simulations. Also, under the influence of different control gain conditions, density wave characteristics for traffic flow system with time delay are intuitively shown. The results indicate that time delay effect in sensing density and flux information can aggravate traffic congestion, and traffic congestion will be effectively relieved by considering steady flow control signal. [ABSTRACT FROM AUTHOR]

In this short paper we tackle two subjects. First, we provide a lower bound for the first eigenvalue of the antiperiodic problem for a Hill's equation based on L p -conditions, and as a consequence, we introduce an adjusted statement of the main result about the asymptotic stability of periodic solutions for the general Duffing equation in (Torres in Mediterr. J. Math. 1(4):479–486, 2004) (Theorem 4). This appropriate version of the result arises because of one subtlety in the proof provided in (Torres in Mediterr. J. Math. 1(4):479–486, 2004). More precisely, the lower bound of the first antiperiodic eigenvalue associated with Hill's equations of potential a (t) employed there may be negative, thus the conclusion is not completely attained. Hence, the adjustments considered here provide a mathematically correct result. On the other hand, we apply this result to obtain a lateral asymptotic stable periodic oscillation in the Comb-drive finger MEMS model with a cubic nonlinear stiffness term and linear damping. This fact is not typical in Comb-drive finger devices, thus our results could provide a new possibility; a new design principle for stabilization in Comb-drive finger MEMS. [ABSTRACT FROM AUTHOR]

In this paper, an uncertain nonlinear switched system is actually a nonlinear switched system disturbed by subjective uncertainties, usually written as several uncertain differential equations. Stability analysis of switched systems has been discussed in depth, while few results about stability of uncertain switched systems were published before. To fill this gap, stability in measure and asymptotic stability of uncertain nonlinear switched systems with countable switches in infinite-time horizon are both considered. The essential property of the solutions to such uncertain switched systems will be illustrated and captured from different perspectives with the help of the above stability analysis. Two theorems to judge these stabilities are proposed and then verified according to uncertainty theory and Lyapunov's second method. At last, a practical model of population growth is studied to display the validness of the results derived. [ABSTRACT FROM AUTHOR]

In this paper, a novel strategy of extending the domain of attraction of an asymptotically stable, affine nonlinear system is proposed. This method is based on the concept of mapping and relies on the asymptotic stability of a nonlinear system image via a continuous and injective mapping. The goal of designing the controller is to map the domain of attraction of an open-loop system into a larger domain, which is the domain of attraction of a closed-loop system. To find a suitable mapping that can make desired changes in the shape and size of domain of attraction, a criterion is obtained and its implementation instruction is demonstrated by examples. Results of simulation provided demonstrate the efficiency of the method proposed. [ABSTRACT FROM AUTHOR]

In this paper, we have derived a discrete evolutionary Beverton–Holt population model. The model is built using evolutionary game theory methodology and takes into consideration the strong Allee effect related to predation saturation. We have discussed the existence of the positive fixed point and examined its asymptotic stability. Analytically, we demonstrated that the derived model exhibits Neimark–Sacker bifurcation when the maximal predator intensity is at lower values. All chaotic behaviors are justified numerically. Finally, to avoid these chaotic features and achieve asymptotic stability, we implement two chaos control methods. [ABSTRACT FROM AUTHOR]

In this paper, a weakly coupled system (by the displacement of symmetric type) consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain is considered. Under the assumptions on a more general type of relaxation functions, an explicit and general decay rate result is established by using the multiplier method and some properties of the convex functions. [ABSTRACT FROM AUTHOR]