Role of Allee and Fear for Controlling Chaos in a Predator–Prey System with Circulation of Disease in Predator

Abstract

This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey’s growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter ([Formula: see text]) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter?