Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect

Abstract

This paper is concerned with a prey–predator system involving herd behaviour and strong Allee effect. First, the local stability analysis of all the possible equilibrium points are investigated. Second, the existence of Hopf bifurcation around the unique positive equilibrium are carried out. Finally, this paper is ended with a numerical simulation to understand the dynamics of the system. As it turns out that the ‘Allee effect constant’ plays a very important role in biological invasion mechanism, such as controlling and preventing biological invasion or invading successfully.

Keywords

• Prey–predator
• stability
• Hopf bifurcation
• invasion mechanism