A Modified Leslie–Gower Model Incorporating Beddington–DeAngelis Functional Response, Double Allee Effect and Memory Effect

In this paper, a modified Leslie–Gower predator-prey model with Beddington–DeAngelis functional response and double Allee effect in the growth rate of predator population is proposed. order to consider memory on proposed model, we employ Caputo fractional-order derivative. We investigate dynamic behaviors for both strong weak cases. The existence, uniqueness, non-negativity, boundedness solution are discussed. Then, determine existing condition local stability analysis all possible equilibrium points. Necessary conditions existence Hopf bifurcation driven by fractional derivative also determined analytically. Furthermore, choosing suitable Lyapunov function, derive sufficient ensure global asymptotic extinction point case as well prey interior case. Finally, numerical simulations shown confirm theoretical results can explore more dynamical system, such bi-stability forward bifurcation.