双状态切换下BVP振子的复杂行为分析

发布时间：2018-03-20 04:13

  本文选题：切换系统　切入点：广义BVP振子　出处：《力学学报》2016年04期 　论文类型：期刊论文

【摘要】：非线性切换系统具有广泛的工程背景,而传统的非线性理论不能直接用来解决其中的问题,因而成为当前国内外热点和前沿课题之一.目前相关工作大都是围绕固定时间或单状态切换开展的,而实际工程系统大都属于多状态切换问题,同时多状态切换涉及到更为丰富的动力学行为.本文基于两广义BVP振子,通过引入双向切换开关,构建了双状态切换下的非线性动力学模型,进而研究状态切换导致的各种运动模式及其相应的产生机制.应用非光滑系统的Poincar′e映射理论,推导了双状态切换下的Lyapunov指数的计算公式,结合子系统的分岔分析,得到了切换系统随分岔参数变化的动力学演化过程及其相应的最大Lyapunov指数的变化情况.得到了双状态切换条件下系统存在着各种形式的振荡行为,分析了诸如周期突变等现象及通往混沌的倍周期分岔道路,揭示了不同运动模式的产生机制及倍周期序列的本质.与固定时间切换和单状态切换系统不同,双临界状态切换系统存在着更为丰富的非线性现象,其主要原因在于双状态切换会产生更多的切换点,且切换点的位置更加多变.同时切换系统的倍周期分岔序列与光滑系统中的倍周期分岔序列不同,切换系统的倍周期分岔序列只对应于切换点数目的成倍增加,而其相应的周期一般不对应于严格的周期倍化过程.
[Abstract]:Nonlinear switched systems have a wide engineering background, but the traditional nonlinear theory can not be directly used to solve the problems. Therefore, it has become one of the hot and frontier topics at home and abroad. At present, most of the related work is carried out around fixed time or single state switching, but the practical engineering systems are mostly multi-state switching problems. At the same time, multi-state switching involves a richer dynamic behavior. Based on two generalized BVP oscillators, a nonlinear dynamic model with two-state switching is constructed by introducing bi-directional switching switches. Based on the Poincar'e mapping theory of non-smooth systems, the calculation formula of Lyapunov exponent under two-state switching is derived, and the bifurcation analysis of subsystems is combined with the analysis of the bifurcation of subsystems. The dynamic evolution process of switched systems with bifurcation parameters and the corresponding maximum Lyapunov exponents are obtained. The phenomena such as periodic mutation and the path of periodic doubling bifurcation to chaos are analyzed. The generation mechanism of different motion modes and the nature of periodic doubling sequence are revealed, which are different from those of fixed time switching and single state switching systems. There are more nonlinear phenomena in the double critical state switched system, the main reason is that the double state switching will produce more switching points. Moreover, the position of the switching point is more changeable. At the same time, the period doubling bifurcation sequence of the switched system is different from that of the smooth system, and the double period bifurcation sequence of the switched system only corresponds to the multiple increase of the number of switching points. However, the corresponding period does not correspond to the strict periodic doubling process.
【作者单位】： 江苏大学土木工程与力学学院;
【基金】：国家自然科学基金(11472115,11572141,1150209) 镇江市科技攻关基金(GY2013032,GY2013052)资助项目
【分类号】：O322
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本文编号：1637448