非周期力在混沌控制中的双重功效

探讨了非周期力（有界噪声或混沌驱动力）在非线性动力系统混沌控制中的影响.以一类典型的含有五次非线性项的Duffing-van der Pol系统为范例，通过对系统的轨道、最大Lyapunov指数、功率谱幅值及Poincar截面的分析，发现适当幅值的有界噪声或混沌信号，一方面可以消除系统对初始条件的敏感依赖性，抑制系统的混沌行为，将系统的混沌吸引子转化为奇怪非混沌吸引子；另一方面也可以诱导系统的混沌行为，将系统的周期吸引子转化为混沌吸引子.从而揭示了非周期力在混沌控制中的双重功效：抑制混沌和诱导混沌. 关键词： 混沌控制 有界噪声 混沌驱动力

The twofold influence of non-periodic force on chaos control

The influences of a kind of non-periodic force，modeled by bounded noise or chaotic driving，on chaos control of nonlinear dynamical system are studied. Suppressing chaos as well as inducing chaos in a periodically driven Duffing-van der Pol oscillator with 5 nonlinear components is studied in detail. By examining the separation distance，the largest Lyapunov exponent，the scaling exponent of power spectrum, and the Poincar map of the considered oscillator，it is found that the non-periodic driving of appropriate amplitude，on one hand，can eliminate the sensitive dependence on initial conditions，then suppress the chaotic behavior and convert a chaotic attractor to a strange but nonchaotic one in this DVP oscillator. On the other hand，it can induce the chaotic behavior and then convert a periodic attractor to a chaotic one as well. Thus，the dual roles of non-periodic driving，i.e. suppressing and inducing chaos，in chaos control of nonlinear dynamical systems are revealed.