中文摘要：

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.

英文摘要：

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 Poincar6 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 nonehaotic 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.