Zhidong Teng

Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predator

Abstract In this paper, a delayed predator–prey system with stage structure for predator is proposed and studied. It is found that the time delay is harmless for permanence of the stage-structured system. If αβ αβ xa0>xa01, we show that the unique positive equilibrium is locally asymptotically stable when time delay τ ∗ is sufficiently small, while loss of stability by a Hopf bifurcation can occur as the delay increases.

Dynamic behavior for a nonautonomous SIRS epidemic model with distributed delays

A nonautonomous SIRS epidemic model with distributed delay is investigated. Two new threshold values, R* and R^* are derived. The model is permanent as R*>1 and R^*<1 implies the extinction of the disease. Using the Liapunov functional method, global behavior of the model is studied.

Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network

Abstract This paper investigates the global Mittag–Leffler stability of coupled system of fractional-order differential equations on network (CSFDEN). By using graph theory and the Lyapunov method, we provide a method for constructing a global Lyapunov function for CSFDEN. Consequently, several sufficient conditions are obtained to ensure the Mittag–Leffler stability of CSFDEN. These criteria have a close relation to the topology property of the network. Finally, a numerical example is presented to demonstrate the validity and feasibility of the theoretical result.

A State Dependent Pulse Control Strategy for a SIRS Epidemic System

With the consideration of mechanism of prevention and control for the spread of infectious diseases, we propose, in this paper, a state dependent pulse vaccination and medication control strategy for a SIRS type epidemic dynamic system. The sufficient conditions on the existence and orbital stability of positive order-1 or order-2 periodic solution are presented. Numerical simulations are carried out to illustrate the main results and compare numerically the state dependent vaccination strategy and the fixed time pulse vaccination strategy.

Threshold conditions for a non-autonomous epidemic model with vaccination

In this article, we wish to investigate the dynamical behaviour of an SIRVS epidemic model with time-dependent coefficients. Under the quite weak assumptions, we give some new threshold conditions which determine whether or not the disease will go to extinction. The permanence and extinction of the infectious disease is studied. When the system degenerates into periodic or almost periodic system, the corresponding sharp threshold results are obtained for permanent endemicity versus extinction in terms of asymptotic time. In order to illustrate our theoretical analysis, some numerical simulations are also included in the end.

Permanence and global attractivity of an impulsive ratio-dependent predator-prey system in a patchy environment

This paper studies an impulsive nonautonomous two species predator-prey Lotka-Volterra type dispersal system in a patchy environment, in which the prey species can disperse among n different patches, but the predator species is confined to one patch and cannot disperse. On the basis of inequality estimation techniques and the comparison theory of impulsive differential equations, sufficient conditions of integrable form for the permanence and extinction are obtained. By constructing appropriate Lyapunov function, conditions for the global attractivity of the system are established.