Intra-Specific Competition in Prey Can Control Chaos in a Prey-Predator Model

Abstract

In this article, we propose a general prey-predator model with the presence of Allee effect in prey. We have considered different competition coefficients within the prey population, which leads to the emergent carrying capacity. The stability analysis of the system is discussed. Further, the dynamical behavior of the system is analyzed, taking delay and emergent carrying capacity as bifurcation parameters. Time delay can turn a stable equilibrium into an unstable one. It was shown that our system experiences the Hopf bifurcation, as the delay parameter crosses some critical values. Further increases in delay produce chaos, which can be controlled by the emergent carrying capacity.