Global attractivity in time-delayed predator-prey systems

Permanence and Global Attractivity of a Delayed Discrete Predator-Prey System with General Holling-Type Functional Response and Feedback Controls

Recommended by Leonid Berezansky This paper discusses a delayed discrete predator-prey system with general Holling-type functional response and feedback controls. Firstly, sufficient conditions are obtained for the permanence of the system. After that, under some additional conditions, we show that the periodic solution of the system is global stable.

The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parame...

Periodic Solutions in Periodic Delayed Gause-Type Predator-Prey Systems

Reasonable sufficient conditions are obtained for the existence of positive periodic solutions in periodic delayed Gause-type predator-prey systems. Our approach involves the application of coincidence degree theorem and estimations of uniform upper bounds on solutions. This method imposes minimum restrictions on the form and magnitude of time delays. Indeed, our results are applicable to discr...

Global Attractivity and Periodic Solution of a Discrete Multispecies Cooperation and Competition Predator-Prey System

Permanence and Global Attractivity of a Discrete Two-Prey One-Predator Model with Infinite Delay

Correspondence should be addressed to Zhong Li, [email protected] Received 4 February 2009; Revised 2 July 2009; Accepted 15 August 2009 Recommended by Leonid Berezansky A discrete two-prey one-predator model with infinite delay is proposed. A set of sufficient conditions which guarantee the permanence of the system is obtained. By constructing a suitable Lyapunov functional, we also obtain ...