Fengde Chen

Stability analysis of a prey-predator model with holling type III response function incorporating a prey refuge

In this paper, we consider a prey-predator model with Holling type III response function incorporating a prey refuge. The purpose of the work is to offer mathematical analysis of the model and to discuss some significant qualitative results that are expected to arise from the interplay of biological forces. Some numerical simulations are carried out.

Positive periodic solutions of neutral Lotka-Volterra system with feedback control

With the help of a continuation theorem based on Gaines and Mawhins coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of neutral Lotka-Volterra system with periodic delays and feedback control. Our results extend and improve existing results, and have further applications in population dynamics.

Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition predator-prey systems

In this paper, we propose a discrete multispecies Lotka-Volterra competition predator-prey systems. For general non-autonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; for periodic case, sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained.

Almost periodic solution for a Volterra model with mutual interference and Beddington-DeAngelis functional response

In this paper, we consider a Volterra model with mutual interference and Beddington-DeAngelis functional response. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

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

In this paper, a discrete N-species cooperation system with time delays and feedback controls is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

Global attractivity in an almost periodic multi-species nonlinear ecological model

Abstract A nonlinear almost periodic predator–prey model with n-preys and m-predators is studied in this paper, which can be seen as the modification of the traditional multi-species Lotka–Volterra predator–prey model. For general nonautonomous case, by using the differential inequality theory, we obtain the sufficient conditions which guarantee the uniform persistence and nonpersistence of the system; After that, by constructing a suitable Lyapunov function, some sufficient conditions are obtained which ensure the global attractivity of the system. For almost periodic case, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the existence of an unique globally attractive positive almost periodic solution of the system are obtained. Examples together with their numeric simulations show the feasibility of our main results.

Permanence in nonautonomous multi-species predator-prey system with feedback controls

A nonautonomous multi-species predator-prey system with feedback controls is proposed in this paper, where the competition among the predator species and among the prey species is considered, also some important factors such as the effect of toxins and the age-structure are also considered. Average conditions are obtained for permanence and global attractivity in the system. The results obtained here generalized the main results of Zhao and Jiang [J.D. Zhao, J.F. Jiang, Permanence in nonautonomous Lotka-Volterra system with predator-prey, Appl. Math. Computat.,152 (2004) 99-109].

Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances

In this paper, we consider a nonautonomous competitive Lotka-Volterra system of two species with the effect of toxic substances. It is shown that toxic substances play an important role in the extinction of species. We prove that one of components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation under some conditions.

Global asymptotic stability in n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control

Abstract A non-autonomous Lotka–Volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the system. Some new results are obtained.

On a periodic multi-species ecological model

A periodic predator-prey model with m-predators and n-preys is proposed in this paper, which can be seen as the modification of the traditional Lotka-Volterra model. By using comparison theorem, the ultimately bounded region of the system is obtained. By using comparison theorem and Brouwer fixed point theorem, sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained. Finally, by constructing a suitable Lyapunov function, some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system. The results obtained here generalized the main results of [J.D. Zhao, W.C. Chen, Global asymptotic stability of a periodic ecological model, Applied Mathematics and Computation, 147(3) (2004), 881-892].