国家自然科学基金资助项目（10432010，10172011）
对一类具有状态反馈控制的脉冲动力系统的动力学性质进行了研究.由周期解的扰动解得到了一个Poincare映射，利用Poincare映射讨论了系统周期解的分岔,并得到了半平凡周期解和正周期1解存在和稳定的充分条件.定性分析和数学模拟表明, 半平凡周期解通过fold分岔分岔出正周期1解,正周期1解通过flip分岔分岔出正周期2解,再通过一系列flip分岔通向混沌.此外，讨论了脉冲状态反馈控制的效果.
The dynamics of a class of impulsive dynamic systems with impulsive state feedback control was studied. A Poincare map was constructed to discuss the bifurcation of periodic solution,and the sufficient conditions for the existence and stability of semitrivial periodic solution and positive period1 solution were obtained. The qualitative analysis and numerical results show that a positive period1 solution bifurcates from the semitrivial periodic solution through a fold bifurcation, a positive period2 solution bifurcates from the positive period1 solution through a flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. The superiority of the state feedback control strategy was also discussed.
蒋贵荣,陆启韶,钱临宁.一类脉冲动力系统的状态反馈控制[J].动力学与控制学报,2005,3(4):17~23; Jiang Guirong, Lu Qishao, Qian Linning. State feedback control of a class of impulsive dynamic systems[J]. Journal of Dynamics and Control,2005,3(4):17-23.
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