Dynamical complexities in a discrete-time predator-prey system as consequences of the weak Allee effect on prey

[摘要] In this paper, a two dimensional discrete-time predator-prey system with weak Allee effect, affecting the prey population, is considered. The existence of the positive fixed points of the system and topological classification of coexistence positive fixed point are examined. By using the bifurcation theory, it is shown that the discrete-time predator-prey system with Allee effect undergoes Flip and Neimark-Sacker bifurcations depending on the parameter a. The parametric conditions for existence and direction of bifurcations are investigated. Numerical simulations including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the system are performed to validate analytical results. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behavior in the considered system. Finally,the OGY feedback control method is implemented to stabilize chaos existing in the system.

[学科分类] 数学（综合）

[关键词] predator-prey system;fixed point;stability;flip bifurcation;Neimark-Sacker bifurcation;chaotic behavior;OGY feedback control method