Diffusion-driven instability and pattern formation in a prey-predator model with fear and Allee effect

Abstract

This paper analyses a predator-prey model with Holling type II response function incorporating Allee and fear effect in the prey. The model includes intra species competition among predators. We find out the local dynamics as well as Hopf bifurcation by considering level of fear as bifurcation parameter. The condition for diffusion-driven instability and patterns are then demonstrated in relation to the system's ecological parameters and diffusion coefficients. Intra-specific competition affects the dynamics of the system and Turing pattern formation. Moreover, output of results is verified through numerical simulation. Thus, from a dynamical standpoint, the considered model seems to be relevant in the field of ecology.

Keywords

• allee effect
• ear effect
• diffusion
• hopf bifurcation
• turing instability
• pattern.