Dynamical Property Analysis of a Delayed Diffusive Predator-Prey Model with Fear Effect (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we study a delayed diffusive predator-prey modelwith fear effect and Holling II functional response. The stability of the positive equilibrium is investigated. We find that time delay can destabilize thestable equilibrium and induce Hopf bifurcation. Diffusion may lead to Turing instability and inhomogeneous periodic solutions. Through the theory ofcenter manifold and normal form, some detailed formulas for determining theproperty of Hopf bifurcation are presented. Some numerical simulations arealso provided.
Keywords: Delay; Diffusion; Predator-prey; Turing instability; Hopf bifurcation.