线性脉冲哈密顿系统的分岔分析和控制

Bifurcation and bifurcation control in a linear Hamiltonian impulsive system

通过将非线性形式的脉冲引进到线性哈密顿系统里,离散映射、利用中心流形理论和分岔理论讨论了线性脉冲哈密顿系统的复杂动力学性质。理论上分析了系统周期-1解的存在和稳定的条件、flip分岔的分岔条件,设计了一个线性脉冲控制器控制系统的动力学行为,给出了能验证理论分析结果的数值结论。

In this paper,the complex dynamical behavior of linear Hamiltonian impulsive system is discussed by using discrete map,center manifold theorem and bifurcation theorem.The existence and stability of the positive period solution of this system are investigated.The condition of occurrence for filp bifurcation is derived.A linear impulsive controller is proposed to control the dynamical behavior of system.The numerical results for bifurcation and bifurcation control,which are illustrated with two examples,are in good agreement with the theoretical analysis.