【摘要】 研究了一类具有HollingⅣ型功能反应和状态反馈控制的捕食模型,利用相似的Poincaré准则和半连续动力系统几何理论,得到了半平凡周期解稳定和阶1-周期解存在的充分条件.数值模拟验证了结论的正确性和状态反馈控制的有效性.同时,数值模拟揭示了状态反馈控制系统存在着丰富的动力学行为,比如fold分岔、flip分岔和混沌现象.更多还原

【Abstract】 A class of predator-prey systems with Holling Ⅳ functional responses under state feedback control were studied. The sufficient conditions for the existence and stability of semi-trivial solutions and order-1 periodic solutions were obtained by means of the analogue of the Poincaré criterion and the geometric theory for semi-continuous dynamical systems. The numerical simulation verifies the correctness of the conclusion and the effectiveness of the state feedback control, and reveals abundant dynamic behaviors of the state feedback control system, such as the fold bifurcation, the flip bifurcation and chaos.更多还原