一类自治脉冲微分方程的动力学研究  

DYNAMICS OF A CLASS OF AUTONOMOUS IMPULSIVE EQUATIONS

作　　者：钱临宁[1] 陆启韶[1] 

机构地区：[1]北京航空航天大学理学院数学系,北京100083

出　　处：《动力学与控制学报》2008年第2期97-101,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10572011)~~

摘　　要：对一类自治脉冲微分方程的动力学性质进行了研究,给出了半平凡周期解的存在与稳定的充分条件,建立Poincaré映射将周期解问题转化为不动点问题.理论分析及数值模拟表明,半平凡周期解通过跨临界分岔获得稳定的正周期-1解.数值模拟显示,随着控制参数的变化,正周期-1解通过倍周期分岔出正周期-2解,再通过一系列倍周期分岔通向混沌.The dynamics of a class of autonomous impulsive differential equation was studied, and the sufficient conditions for the existence and stability of a semi - trivial periodic solution were obtained. The problem of periodic solution was transformed into a fixed - point problem by constructing the Poncare map. Theoretical analysis and numerical results show that a steady positive period - 1 solution bifurcates from the semi - trivial periodic solution through a transcrifical bifurcation. And the numerical results also show that,when the control parameter varies, a positive period -2 solution bifurcates from the positive periodic solution through a flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations.

关 键 词：脉冲动力系统 自治脉冲微分方程 跨临界分岔 周期解 

分 类 号：O175[理学—数学]