Abstract
We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of the model and show the existence of Hopf bifurcation at the positive equilibrium under some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theorem.
Highlights
The dynamic relationship between predators and their preys has long been and will continue to be one of dominant themes in both ecology and mathematical ecology due to its universal existence and importance
We show the bifurcation diagram to display the distribute of the positive roots; in Figure 1, the whole region has been divided into six parts; the number indicates the number of positive equilibria
We have considered a modified version of Leslie-Gower model with Holling-type II functional and delayed diffusive predator-prey model under homogeneous
Summary
The dynamic relationship between predators and their preys has long been and will continue to be one of dominant themes in both ecology and mathematical ecology due to its universal existence and importance. A major trend in theoretical work on prey-predator dynamics has been to derive more realistic models, trying to keep to maximum the unavoidable increase in complexity of their mathematics [1]. In this optic, recent years, the important Leslie-Gower predator-prey model [2, 3] has been extensively studied in [4,5,6,7]. The reproduction of the individuals is modeled by diffusion with diffusion coefficients D1 > 0 and D2 > 0 for the prey and predator, respectively This basic model is described by a system of two partial differential equations:.
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