Bifurcation analysis and chaos control of a discrete-time prey-predator model with Allee effect

Abstract

In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for local asymptotic stability of fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support theoretical results.