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

Year 2023, , 1029 - 1045, 15.08.2023

Özlem Ak Gümüş

https://doi.org/10.15672/hujms.1179682

Cited By: 1

Abstract

In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for the local asymptotic stability of the 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 the theoretical results.

Keywords

prey-predator model, fixed point, stability, bifurcation theory, Neimark-Sacker bifurcation, chaos control, flip bifurcation

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