The stability and bifurcation of homogeneous diffusive predator–prey systems with spatio–temporal delays

Abstract

<p style='text-indent:20px;'>In this paper, we consider a generalized predator-prey system described by a reaction-diffusion system with spatio-temporal delays. We study the local stability for the constant equilibria of predator-prey system with the generalized delay kernels. Moreover, using the specific delay kernels, we perform a qualitative analysis of the solutions, including existence, uniqueness, and boundedness of the solutions; global stability, and Hopf bifurcation of the nontrivial equilibria.</p>