具性别结构时滞捕食系统的Hopf分支,混沌与脉冲控制

Hopf Bifurcation,Chaos and Impulsive Control in a Sex-structured Prey-predator System with Time Delay

建立了具性别结构的时滞捕食系统,研究了平衡点的存在性及局部稳定性,给出了系统发生局部Hopf分支的充分条件,并应用中心流形定理研究了Hopf分支周期解的性质(分支类型,方向及稳定性).数值例子佐证了理论结果,并揭示了系统诸如高倍周期及拟周期振荡,混沌振荡,倍周期分岔等复杂的动力学行为;脉冲控制可以有效的改善系统的稳定性.

A prey-predator system with sex-structured and time delay is established.The existence and stabihty of the equilibrium points are studied,and the sufficient conditions for the system occurring local Hopf bifurcation are obtained.The properties(type,direction and stability) of the Hopf bifurcating periodic solution analyzed by center manifold theorem.Numerical examples are carried out to illustrate the theoretical results,and shown that the system considered has more complicated dynamics,such as high-order periodic and quasi-periodic oscillations,chaotic oscillations period-doubling bifurcation,etc;and shown that impulsive control which can improve the stabihty of the system effectively.