Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response

Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response

The dynamic relationship between the predator and the prey has long been and will continue to be one of the dominant themes in population dynamics due to its universal existence and importance in nature 1 . In order to precisely describe the real ecological interactions between species such asmite and spidermite, lynx and hare, and sparrow and sparrow hawk, described by Tanner 2 and Wollkind et...

Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response

We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are p...

Periodic solutions for a neutral delay predator-prey model with nonmonotonic functional response

In a classic study of population dynamics, the predator-prey models have been studied extensively. We refer the reader to [1−5] and the references cited therein. Up to the present, most authors just studied systems with monotonic functional response, such as [6,7]. However, the actual living environments of species are not always like this due to the ecological effects of This work was supporte...

Periodic solutions for a predator-prey model with Holling-type functional response and time delays

A delayed periodic Holling-type predator–prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulat...

Positive periodic solutions of neutral predator-prey model with Beddington-DeAngelis functional response