Complexity of a Discrete-Time Predator-Prey Model Involving Prey Refuge Proportional to Predator

Abstract

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.

Keywords

• chaos
• neimark-sacker bifurcation
• predator-prey
• refuge
• stability