This paper deals with a Holling type III diffusive predator-prey model with stage structure and nonlinear density restriction in the space R. We first consider the asymptotical stability of equilibrium points for the model of ODE type. Then, the existence and uniform boundedness of global solutions and stability of the equilibrium points for the model of weakly coupled reactiondiffusion type ar...

Stabilization of a class of systemswith time delay is studied using adaptive control.With the help of the “error to error” technique and the separated “descriptor form” technique, the memory state-feedback controller is designed.The adaptive controller designed can guarantee asymptotical stability of the closed-loop system via a suitable Lyapunov-Krasovskii functional. Some sufficient condition...

In this paper, we study the nonnegative periodic dynamics of the delayed Cohen–Grossberg neural networks with discontinuous activation functions and periodic interconnection coefficients, selfinhibitions, and external inputs. Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy problem. Under some conditions, the existence and the asymptotical ...

An SI epidemic model with stage structure is investigated. In the model, impulsive biological control is taken, that is, we release infected pests to the field at a fixed time periodically. We get a sufficient condition for the global asymptotical stability of the pesteradication periodic solution (0,0, ̃ I(t)), and a condition for the permanence of the system. At last, a brief discussion shows ...

This paper deals with the problem of delay-dependent stability criterion of uncertain periodic switched recurrent neural networks with time-varying delays.When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach SQLF and freeweighting matrix ...

In the paper, the synchronization stability of a class of complex dynamical networks with non-delayed and delayed coupling is investigated. By establishing impulsive delay differential inequalities, sufficient conditions on the asymptotical stability of complex dynamical networks are derived. Some impulsive controllers are explicitly designed not only to achieve asymptotically stable for the co...

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion ...

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and themethod of successor function, we obtain the systemwith impulsive effects that has an order o...

In this paper, the problem of dynamics analysis for a class of new impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on linear matrix inequality (LMI) forms, which can be easily solved by LMI Toolbox in Matlab. An example is given to show the effectivenes...

Establishing robust asymptotical stability of uncertain systems affected by time-varying uncertainty is a key problem. LMI sufficient conditions have been proposed in the literature for addressing this problem based on homogeneous polynomial Lyapunov functions. Unfortunately, till now it has been unclear whether these conditions are also necessary. This paper proposes a proof in order to show t...