Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect

Abstract

In this paper, a delayed diffusive predator-prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results.

Stability Analysis of a Stage-Structure Predator–Prey Model with Holling III Functional Response and Cannibalism

“…Time delays have been widely used to describe the influence of a population on its status in biological systems. In physics, ecology, biology, and other applications, delay differential equations are often more practical than ordinary differential equations since a time delay could cause a stable equilibrium to become unstable and cause the population to fluctuate [1][2][3][4][5][6][7].…”

Stability and Bifurcation for a Delayed Diffusive Two‐Zooplankton One‐Phytoplankton Model with Two Different Functions

“…is spatial diffusion is subject to Fick's law. erefore, the influence of spatial diffusion on the phytoplankton-plankton model has been paid more attention by many scholars [35][36][37][38][39][40][41][42][43][44][45]. In the work by Jia et al [46], a three-component plankton model with spatial diffusion and time delay is proposed, which describes the relationship between a zooplankton and two phytoplankton.…”