Stability of fractional-order prey–predator system with time-delay and Monod–Haldane functional response

Abstract

In this paper, we study the dynamics of a fractional-order delayed prey–predator system with Monod–Haldane response function. The model describes the interaction between prey and two populations of predator species: immature or juvenile and mature or adult predator. A single time delay is incorporated in the model to justify the gestation period of adult predator. The existence of solutions, steady states, and sufficient conditions to ensure the asymptotic stability of the steady states are investigated. Global stability around the interior equilibrium point by constructing the suitable Lyapunov functional is also investigated. The system displays Hopf bifurcation depending on the conversion coefficient (prey to immature predator) and time delay. The fractional-order derivatives in the model develop the stability results of solutions and improve the model behaviors. Finally, some numerical simulations are given to verify the success of derived theoretical results.