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摘要: 利用Silnikov定理，讨论了具有自动频率跟踪功能电磁振动机械系统的混沌特性.借助卡尔达诺公式和微分方程组级数解分别讨论了该系统的特征值问题和同宿轨道的存在性，进而比较严密地证明了该系统Silnikov型Smale混沌的存在性，并给出发生Silnikov型Smale混沌所需条件.利用数值模拟得到该类机电耦合系统的相轨迹图、Lyaponov指数谱和Lyaponov维数，进一步验证了该非线性系统存在奇怪吸引子.
Abstract: Based on the Silnikov criterion, the chaotic properties of mechanically and electrically coupled nonlinear dynamical systems were discussed. Using Cardano formula and series solution of differential equation, the eigenvalue problem and existence of homoclinic orbit were studied respectively. A rigorous proof of the existence of Silnikov-sense Smale horseshoe chaos was presented and some conditions leading to chaos were obtained. The space trajectory, Lyapunov exponent and Lyapunov dimension were investigated via numerical simulation, which showed that chaotic attractors exist in the non-linear dynamical systems.
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