一类具有反馈控制与多变时滞Nicholson’s Blowflies模型的持久性（英文）

This paper covers the dynamic behaviors for a class of Nicholson's blowflies model with multiple time-varying delay and feedback control. By using the differential inequality theory, a set of sufficient conditions are obtained to ensure the permanence of the system.Our result shows that feedback control variables have no influence on the permanence of the system.     

On a mutualism model with feedback controls

We propose and study a mutualism model with feedback controls. By applying a new differential inequality, we show that the conditions which ensure the permanence of the system are the same as that of the model without feedback controls, which means that the feedback control variables have no influence on the persistent property of the system. Our results not only improve but also complement some existing ones.     

Extinction in a nonautonomous competitive system with toxic substance and feedback control

This paper deals with a nonautonomous competitive system with infinite delays and feedback control. Sufficient conditions for the permanence of the system are first obtained. By constructing a suitable Lyapunov function, we obtain the sufficient conditions which guarantee that one of the components is driven to extinction. Our result shows that feedback control have an influence on the extinction of the system. Examples together with their numerical simulations illustrate the feasibility of our main results.     

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.     

Almost sufficient and necessary conditions for permanence and extinction of nonautonomous discrete logistic systems with time-varying delays and feedback control

A class of nonautonomous discrete logistic single-species systems with time-varying pure-delays and feedback control is studied. By introducing a new research method, almost sufficient and necessary conditions for the permanence and extinction of species are obtained. Particularly, when the system degenerates into a periodic system, sufficient and necessary conditions on the permanence and extinction of species are obtained. Moreover, a very important fact is found in our results, that is, the feedback control and delays are harmless for the permanence and extinction of species for discrete single-species systems. This shows that in a discrete single-species system introducing the feedback control to factitiously control the permanence and extinction of species is useless.     

PERMANENCE OF A DISCRETE SINGLE SPECIES SYSTEM WITH DELAYS AND FEEDBACK CONTROL

In this paper,a discrete single species system with time delays and feedback control is considered.Sufficient conditions which guarantee the permanence of all positive solutions to this discrete system are obtained.The results show that the feedback control is harmless for the permanence of the species.     

Permanence for a nonautonomous discrete single-species system with delays and feedback control

A nonautonomous discrete single-species system with delays and feedback control is studied. New sufficient conditions for ensuring the permanence of the system are obtained. A very important fact is found in our results, that is, that the feedback control is harmless to the permanence of species. The corresponding results given in [F.D. Chen, Permanence of a single species discrete model with feedback control and delay, Appl. Math. Lett. 20 (2007) 729–733] are improved and extended.     

PERMANENCE IN A SINGLE SPECIES NON-AUTONOMOUS SYSTEM WITH PURE-DELAY AND FEEDBACK CONTROL

In this paper, we consider a single species non-autonomous system with pure-delay and feedback control. Sufficient conditions of integrable form for the permanence of species are established.     

具时滞和反馈控制的修正Leslie-Gower离散系统的持久性

提出并研究具有反馈控制变量和Holling-Ⅱ类功能性反应的修正Leslie-Gower离散捕食系统的持久性问题,通过运用差分不等式得到了一组保证该系统持久的充分性条件．该结果表明反馈控制变量不会影响系统的持久性从而改进了已有的结果．数值模拟显示了本文结果的可行性．     

The permanence and global attractivity of a Kolmogorov system with feedback controls

In this paper, we study the permanence and global asymptotic behavior for a Kolmogorov system with feedback controls. By means of lower and upper averages of a function, the average conditions for permanence, global attractivity and extinction of this system are established respectively. The corresponding results given by Chen in [F. Chen, The permanence and global attractivity of Lotka–Volterra competition system with feedback controls, Nonlinear Anal. 7 (2006) 133–143] and Zhao in [J.D. Zhao, J.F. Jiang, A.C. Lazer, The permanence and global attractivity in a nonautonomous Lotka–Volterra system, Nonlinear Anal. Real World Appl. 5 (2004) 265–276] are extended and improved.     

Permanence of the nonautonomous competitive systems with infinite delay and feedback controls

We study the permanence of a class of nonautonomous two-species Lotka–Volterra competitive systems with infinite delay and feedback controls. New results on the permanence of solutions are obtained. The corresponding results given in [F. Chen, Z. Li, Y. Huang, Note on the permanence of a competitive system with infinite delay and feedback controls, Nonlinear Anal. RWA 8 (2007) 680–687] are improved and extended.     

EFFECT OF TOXIC SUBSTANCE ON A NONAUTONOMOUS COMPETITIVE SYSTEM

In this paper, we consider a nonautonomous competitive system which is also affected by toxic substances. Some averaged conditions for the permanence of this system are obtained. Our result shows that under some suitable assumption on the coefficients of the system, the toxic has no influence on the permanence of the system. Also, by using a suitable Lyapunov function, sufficient conditions which guarantee the attractivity of any two positive solutions of the system are obtained.     

Permanence and global attractivity for discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls

A discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls is proposed and investigated. By using the method of discrete Lyapunov functionals, new sufficient conditions on the permanence of species and global attractivity of the system are established. Particularly, an interesting fact is found in our results, that is, the feedback controls are harmless to the permanence of species for the considered system.     

Permanence and stability in multi-species non-autonomous Lotka–Volterra competitive systems with delays and feedback controls

In this paper, we consider a multi-species Lotka–Volterra type competitive system with delays and feedback controls. A general criteria on the permanence is established, which is described by integral form and independent of feedback controls. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solution to the model.     

Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control

In this paper, we consider a discrete delay logistic equation with feedback control. By applying the theory of difference inequality and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic sequence solution of the system are obtained. The result of this paper is completely new. An example is employed to illustrate our main result.     

一个离散的比率依赖Holling-Ⅲ捕食一食饵系统的持久性

本文研究了一个带有Honing-Ⅲ类功能反应和时间延迟的离散半比率依赖捕食一食饵系统，得到了该态系统永久持续生存的充分条件。     

一类具有时滞和反馈控制的非线性离散模型的持久性

研究了一类具有时滞和反馈控制的非线性单种群离散模型的持久性,获得了该系统持久的充分条件,并通过例子表明结果的可行性,所得结果推广了已有文献的相关结果.     

PERMANENCE OF GENERAL NONAUTONOMOUS SINGLE-SPECIES KOLMOGOROV TYPE SYSTEM WITH DELAY AND FEEDBACK CONTROLS

In this paper, we consider the general nonautonomous single-species Kolmogorov type system with delay and feedback controls. Sufficient conditions for the permanence of species are established. Our results generalize some known results.     

PERMANENCE AND GLOBAL STABILITY OF A FEEDBACK CONTROL SYSTEM WITH DELAYS

This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.     

PERMANENCE AND GLOBAL ATTRACTIVITY OF N-SPECIES COOPERATION SYSTEM WITH DISCRETE TIME DELAYS AND FEEDBACK CONTROLS

In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system.