Multiple Bifurcations in a Discrete Holling–Tanner Predator–Prey Model With Allee Effect and Beddington–DeAngelis Functional Response
TL;DR
This work examines a discretized Holling–Tanner predator–prey model with Beddington–DeAngelis functional response with Allee effect, incorporating the Allee effect on prey populations, providing important insights into how the Allee effect influences ecological systems.
Abstract
This work examines a discretized Holling–Tanner predator–prey model with Beddington–DeAngelis functional response, incorporating the Allee effect on prey populations. A comprehensive analysis of the existence of all fixed points and local stability is carried out. The model exhibits multiple bifurcations of codimension‐1, including the flip and Neimark‐Sacker bifurcations. Furthermore, at a positive fixed point, codimension‐2 bifurcations such as strong resonances , , and are presented. Numerical simulations reveal the presence of chaotic behavior under specific parametric conditions. The OGY chaos control method is employed to manage chaos and stabilize the system in order to address this instability. The findings provide important insights into how the Allee effect influences ecological systems, expanding our understanding of the chaotic fluctuations in predator–prey interactions and population stability. Our analytical conclusions are supported by a detailed numerical simulation that includes stability zones, bifurcation curves in and , phase plots, and the maximal lyapunov exponent.