一个三时滞生物捕食被捕食系统分岔的混合控制

针对多时滞捕食被捕食系统的Hopf分岔控制问题,提出一种基于状态反馈和参数调节的混合控制方法,这种混合控制方法可以延迟有害Hopf分岔的发生或使Hopf分岔消失.分析了该控制系统的稳定性和Hopf分岔的存在性,并通过规范型理论和中心流形定理,给出了分岔周期解的稳定性和分岔方向的计算公式.最后通过数值模拟验证了该理论的正确性.关键词：时滞捕食被捕食系统Hopf分岔混合控制

Hybrid control of bifurcation in a predator-prey system with three delays

The problem of Hopf bifurcation control for a predator-prey system with three delays is considered. A new hybrid strategy is proposed to control the Hopf bifurcation, in which the state feedback and parameter perturbation are used to delay the onset of an inherent bifurcation or make the bifurcation disappear. The stability and the existence of bifurcation are researched. In particular, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form theory and center manifold theorem. Finally, numerical simulation results confirm that the new hybrid controller is efficient in controlling Hopf bifurcation.