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Bifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor
Ceyu Lei1, Xiaoling Han1, Weiming Wang2
1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China.
Abstract:
In this paper, we investigate the complex dynamics of a classical discrete-time prey-predator system with the cost of anti-predator behaviors. We first give the existence and stability of fixed points of this system. And by using the central manifold theorem and bifurcation theory, we prove that the system will experience flip bifurcation and Neimark-Sacker bifurcation at the equilibrium points. Furthermore, we illustrate the bifurcation phenomenon and chaos characteristics via numerical simulations. The results may enrich the dynamics of the prey-predator systems.
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