A fractional-order predator–prey model with Beddington–DeAngelis functional response and time-delay

Abstract

Herein, we propose a fractional-order prey–predator dynamical system with Beddington–DeAngelis type functional response and time-delay. We study the existence of various equilibrium points, and sufficient conditions that ensure the local asymptotic stability of the steady states of such system. The system shows a Hopf-bifurcation which depends on the time-delay. The presence of fractional-order and time-delay in the differential model improves the stability of the solutions and enriches the dynamics of the model. Some numerical examples and simulations are provided to validate the derived theoretical results.