Prey-Predator System; Having Stable Periodic Orbit

Stabilization for a Periodic Predator-Prey System

the predator-prey discrete system codimention- 2 bifurcations

A discrete predator-prey system is presented. We study the existence and stability of the fixed point system. The conditions of existence of Flip and Neimark-sacker bifurcation is the system are derived. By using numerical continuation methods and MatContM toolbox. We compute bifurcation curves of fixed points and cycles with periods up to 32 under variation of one and to parameters, and comput...

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...

Nonexistence of Periodic Orbits for Predator-prey System with Strong Allee Effect in Prey Populations

We use Dulac criterion to prove the nonexistence of periodic orbits for a class of general predator-prey system with strong Allee effect in the prey population growth. This completes the global bifurcation analysis of typical predator-prey systems with strong Allee effect for all possible parameters.

Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results. Copyright q 2008 Can-Yun Huang et al. This is an open acce...

On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

and Applied Analysis 3 To the best of the authors’ knowledge, for the nonautonomous case of predatorprey systems with two predators which consume immature prey and stage structure for prey, whether one could obtain the sufficient and necessary conditions which insure the permanence of the system or not is still an open problem. The aim of this paper is, by further developing the analysis techni...