A Mathematical Modelling Approach for a Past-Dependent Prey-Predator System

Abstract

A memory dependent prey-predator model incorporating Allee effect in prey is analysed. For a small and high values of memory rate, the dynamical changes in the prey and predator densities are demonstrated. The equilibria of the proposed model and the local stability analysis corresponding to each equilibrium are presented. The variables of prey and predator species with respect to memory rate are investigated and the existence of the Hopf bifurcation is shown. The analytical part of this paper is supported with detailed numerical simulations.

Keywords

• nonlinear dynamics
• prey-predator systems
• stability