应用广义胞映射图论方法（GCMD）研究SD（smooth and discontinuous systems）振子的内部激变现象.通过对SD常微分方程系统的全局分析发现周期解通向混沌的内部激变现象是由于周期吸引子与在其吸引域内部的混沌鞍碰撞产生的.混沌鞍是胞空间中的瞬态自循环胞集,周期吸引子与混沌鞍发生碰撞后,混沌鞍转化为混沌吸引子新增的一部分；内部激变不会改变原来吸引域的形状且具有可逆性和对扰动的不敏感性.同时改进广义胞映射图论方法,提出盒子维数的广义胞映射图论方法的近似计算方法.
Abstract:
The interior crisis in the SD(smooth and discontinuous systems) oscillator was studied with the generalized cell mapping digraph method(GCMD). Based on the global analysis of the SD oscillator, we found the road to chaos was due to the collision of the period attractor and the chaotic saddle. Chaotic saddle is the transient selfcycling cell set in the cell state space, after the collision chaotic saddle becomes the new portion of the chaotic attractor. The interior crisis will not change the shape of the basin of attractor, and is invertible and insensitive to the excitation. Simultaneously, the generalized cell mapping digraph method was improved, and a new algorithm was advanced to gain the boxcounting dimension.
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王建华,张晓燕,洪灵. SD振子中内部激变现象的研究[J].动力学与控制学报,2011,9(4):331~336; Wang Jianhua, Zhang Xiaoyan, Hong Ling. Study of the interior crisis in SD oscillator[J]. Journal of Dynamics and Control,2011,9(4):331-336.
