Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity

Abstract

Abstract In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining the property of Hopf bifurcation are given.

Keywords

• Predator–prey
• Delay
• Stability
• Hopf bifurcation