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The study considers the problem of finite-time event-triggered H-infinity consensus for second-order multi-agent systems (MASs) with intrinsic nonlinear dynamics and external bounded disturbances. Based on the designed triggering function, a distributed event-triggered control strategy is presented on the basis of the designed triggering function to ensure consensus in the system, which effectively reduces the data transmission. Then, sufficient conditions for the finite-time consensus with H-infinity performance level of the resulting event-triggered MAS are derived by utilizing the Lyapunov function and finite-time stability theory. Furthermore, Zeno behavior is proven to be excluded under the proposed event-triggered scheme. Finally, the validity of the proposed results is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper investigates a deterministic and stochastic SIQS epidemic model with vertical transmission and Beddington–DeAngelis incidence. Firstly, for the corresponding deterministic system, the global asymptotic stability of disease-free equilibrium and the endemic equilibrium is proved through the stability theory. Secondly, for the stochastic system, the threshold conditions which decide the extinction or permanence of the disease are derived. By constructing suitable Lyapunov functions, we investigate the oscillation behavior of the stochastic system solution near the endemic equilibrium. The results of this paper show that there exists a great difference between the deterministic and stochastic systems, which implies that the large stochastic noise contributes to inhibiting the spread of disease. Finally, in order to validate the theoretical results, a series of numerical simulations are presented. [ABSTRACT FROM AUTHOR]

We present a fractional-order model of two-species facultative mutualism with harvesting. We investigate the stability of the equilibrium points of the model by using the linearization method for noncoexistence of equilibrium points and the Lyapunov direct method for the positive coexistence of an equilibrium point. In addition, we obtain sufficient conditions to ensure the local asymptotic stability and global uniform asymptotic stability for the model. Finally, we provide illustrated numerical examples to verify the stability results obtained in this study. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time anti-synchronization of time-varying delayed neural networks. A simple intermittent adjustment feedback controller is designed to ensure the drive-response systems realize anti-synchronization in a finite time. By employing some differential inequalities and finite-time stability theory, some novel and effective finite-time anti-synchronization criteria are derived based on the Lyapunov functional method. This paper extends some traditional anti-synchronization criteria by using intermittent adjustment feedback control. Finally, two numerical examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose to study a class of discrete schistosomiasis models with general incidence function. This model is derived from a continuous schistosomiasis model (in Appl. Math. 4:1682-1693, 2003) by using the backward Euler discretization method with step size $h=1$ . We visit some basic properties of this discrete model and we study the stabilities of the equilibria by constructing some appropriate Lyapunov functional for the endemic equilibrium. [ABSTRACT FROM AUTHOR]

This paper is concerned with a periodic nonlinear competition model governed by impulsive differential equation with infinitely distributed delays and feedback controls. By means of coincidence degree theory and Lyapunov functional, a set of sufficient criteria are obtained to guarantee the existence and globally asymptotic stability of a unique positive periodic solution of the model. Furthermore, applying our main results to some important competition models which have been well studied in the literature, we establish some new criteria to supplement and generalize some well-known results. [ABSTRACT FROM AUTHOR]

In this paper, a nonautonomous almost periodic prey-predator system with impulsive effects and multiple delays is considered. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals, we derive that there exists a unique almost periodic solution of the system which is uniformly asymptotically stable. Finally, a numerical example and some simulations are presented to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a May cooperative system with feedback controls is proposed and studied. The dynamic behaviors of the system are discussed by using the Lyapunov function method. If $b_{i}\neq0$, $i=1,2$, we show that feedback control variables have no influence on the global stability of the unique positive equilibrium of the system, which means that feedback control variables only change the position of the positive equilibrium and retain its global stability property. If $b_{i}= 0$, $i=1,2$, we can make the system which has a unique globally stable equilibrium or has unboundedly large solutions become globally stable. Some examples are given to illustrate the feasibility of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce stochasticity into a model of SIR with density dependent birth rate. We show that the model possesses non-negative solutions as desired in any population dynamics. We also carry out the globally asymptotical stability of the equilibrium through the stochastic Lyapunov functional method if $R_{0}\le1$. Furthermore, when $R_{0}>1$, we give the asymptotic behavior of the stochastic system around the endemic equilibrium of the deterministic model and show that the solution will oscillate around the endemic equilibrium. We consider that the disease will prevail when the white noise is small and the death rate due to disease is limited. [ABSTRACT FROM AUTHOR]

This paper investigates the coupled systems of stochastic differential equations with variable delays (CSDDEs) on networks. We analyze the existence and uniqueness of solution by combining the method of graph theory with the Lyapunov function analysis. Furthermore, we utilize the graph theory technique and the nonnegative semimartingale convergence theorem to obtain the almost sure stability of sample solutions and the sufficient principles to locate their limit sets, which correlate closely with the topology property of CSDDEs. Finally we illustrate our main results by examples from population dynamics and vibration systems. [ABSTRACT FROM AUTHOR]

The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function. [ABSTRACT FROM AUTHOR]

This paper provides sufficient conditions for absolute stability of an indirect control Lur'e problem of neutral type. The conditions are derived using a Lyapunov-Krasovskii functional and are given in terms of a system of matrix algebraic inequalities. From these matrix inequalities a sufficient condition for linear state feedback stabilizability follows. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of sets for a class of impulsive stochastic functional differential equations. By employing piecewise continuous Lyapunov functions with Razumikhin methods, some sufficient conditions are established to guarantee the stability of sets of impulsive stochastic functional differential equations and we also show that the impulses play an important role in the stability of stochastic functional differential equations. Three examples are presented to illustrate the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

A two species stage-structured commensalism model is proposed and studied in this paper. Local and global stability property of the boundary equilibrium and the positive equilibrium are investigated, respectively. If the stage-structured species is extinct, then depending on the intensity of cooperation, the species may still be extinct or become persistent. If the stage-structured species is permanent, then the final system is always globally asymptotically stable, which means the species is always permanent. Our study shows that increasing the intensity of the cooperation between the species is one of very useful methods to avoid extinction of the endangered species. Such a finding may be useful in protecting the endangered species. An example together with its numeric simulations is presented to verify our main results. [ABSTRACT FROM AUTHOR]

We consider a pathogen dynamics model with antibodies and both pathogen-to-susceptible and infected-to-susceptible transmissions. We consider two types of infected cells, latently infected cells, and actively infected cells. The model considers three types of discrete or distributed delays to characterize the time between the pathogen or the infected cell contacts a susceptible cell and the creation of mature pathogens. We deduct the basic reproduction number and antibody response activation number which determine the existence and stability of the steady states. The global stability analysis of the steady states is established using Lyapunov method. The theoretical results are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the convergence and stability of stochastic parabolic functional differential equations. Firstly, a comparison theorem in the context of Lyapunov-like function together with differential inequality is established. Secondly, various criteria for the convergence and stability are obtained on the basis of the comparison theorem and stochastic analysis techniques. Finally, two examples are provided to illustrate the significance of the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, we propose two techniques for clustering genetic regulatory networks with mixed delays. Laws for identifying coupling parameters are designed, and the Lyapunov theorem and Lipschitz condition are employed to achieve the desired stability and to identify the coupling parameters. Using our proposed methods, the value of a cluster or the sum of clusters can approach the expected values. Numerical examples verify the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guarantee the q-Mittag-Leffler stability and asymptotic stability for the differential systems with q-fractional order. [ABSTRACT FROM AUTHOR]

The robust stability for the impulsive complex-valued neural networks with mixed time delays is considered in this paper. Based on the homeomorphic mapping theorem, some sufficient conditions are proposed for the existence and uniqueness of the equilibrium point. By constructing appropriate Lyapunov–Krasovskii functions and employing modulus inequality techniques, the global robust stability theorem is obtained for the neural networks in complex domain. Finally, numerical simulations confirm the stability of the system and manifest that the complex-valued neural networks work efficiently on storing and retrieving the image patterns. [ABSTRACT FROM AUTHOR]

We study the global stability of endemic equilibrium of an SIS epidemic model with feedback mechanism on networks. The model was proposed by J. Zhang and J. Sun (Physica A 394:24–32, 2014), who obtained the local asymptotic stability of endemic equilibrium. Our main purpose is to show that if the feedback parameter is sufficiently large or if the basic reproductive number belongs to the interval (1,2], then the endemic equilibrium is globally asymptotically stable. We also present numerical simulations to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]