Stability, Neimark-Sacker bifurcation and chaos control for a prey-predator system with harvesting effect on predator

[摘要] This paper deals with the dynamic behavior of a prey predator model obtained by the forward Euler method. We investigate the complex dynamics of discrete-time prey-predator system related to predator population which is subject to the effects of harvesting. The stability of equilibrium point of the model and also the existence and the direction of Neimark-Sacker bifurcation are analyzed. We show that the system undergoes Neimark-Sacker bifurcations by using center manifold theorem and bifurcation theory. A state feedback method is applied in order to control the Neimark-Sacker bifurcation. Moreover, numerical simulations are carried out to demonstrate the theoretical results obtained for stability, bifurcation and chaos control strategy.

[学科分类] 数学（综合）

[关键词] prey-predator system;Neimark-Sacker bifurcation;stability;bifurcation theory;harvesting effect;chaos control