Permanence and global attractivity of an impulsive delay Logistic model

In this paper, we consider an impulsive delay Logistic model. First by mathematical analysis, we obtain the maximum and minimum values of solutions of the corresponding autonomous Logistic model. Then by applying the comparison theorem and constructing some suitable Lyapunov functionals, we discuss the permanence and the global attractivity of the model, based on the boundedness of solutions of the corresponding autonomous Logistic model. An example together with its numerical simulation is given to verify our main result.     

Dynamics of the density dependent predator-prey system with Beddington-DeAngelis functional response

Two models of a density dependent predator-prey system with Beddington-DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained.     

Permanence of a discrete nonlinear N-species cooperation system with time delays and feedback controls

A discrete nonlinear N-species cooperation system with time delays and feedback controls is considered in this paper. Sufficient conditions which ensure the permanence of the system are obtained. It is shown that these conditions are weaker than those of Chen [F.D. Chen, Permanence of a discrete N-species cooperation system with time delays and feedback controls, Appl. Math. Comput. 186(2007) 23-29], that is, our investigation shows that the additional condition in Chen’s paper is not necessary.     

Partial extinction,permanence and global attractivity in nonautonomous <Emphasis Type="Italic">n</Emphasis>-species Lotka-Volterra competitive systems with impulses

In this paper, the qualitative properties of general nonautonomous Lotka-Volterra n-species competitive systems with impulsive effects are studied. Some new criteria on the permanence, extinction and global attractivity of partial species are established by used the methods of inequalities estimate and Liapunov functions. As applications, nonautonomous two species Lotka-Volterra systems with impulses are discussed.     

两斑块间具有非对称双向脉冲扩散的周期单种群模型

研究了两斑块间具有脉冲扩散的周期单种群模型。利用脉冲微分方程的比较原理和一些分析方法,得到了系统持久性的充分条件,然后利用Brouwer不动点理论和构造Lyapunov函数的方法,得到了系统正周期解全局渐近稳定的充分条件。     

具有时滞的非自治Lotka-Volterra竞争系统的持久与灭绝

本文研究具有纯时滞的一般Ｎ－种群非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的持久性和灭绝性．一些新的判别准则被建立．文献［８－１０］中得到的关于无时滞非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的结果被改进和推广．     

Permanence for a delayed periodic predator-prey model with prey dispersal in multi-patches and predator density-independent

In this paper, we study two species time-delayed predator-prey Lotka-Volterra type dispersal systems with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this systems are established. The theoretical results are confirmed by a special example and numerical simulations.     

A stage-structured predator–prey model with disturbing pulse and time delays

In this article we propose a stage-structured predator–prey model with disturbing pulse and time delays and obtain the sufficient conditions for the global attractivity of predator-eradiation periodic solution and permanence of the system. We also show that time delay, pulse catching rate and the period of pulsing can affect the dynamics of the system.     

Permanence of a delayed discrete mutualism model with feedback controls

This paper discusses a two species discrete model of mutualism with delays and feedback controls. Sufficient conditions are obtained for the permanence of the system. The results show that feedback control variables have no influence on the persistence property of the system.