随机参数Duffing系统中的随机混沌及其延迟反馈控制

研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论，将随机Duffing系统转化为与其等效的确定性非线性系统.这样，随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点，并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数，以判别随机Duffing系统的动力学行为.数值计算表明，恰当选取不同的反馈强度和延迟时间，可分别达到抑制或诱发系统混沌的目的，说明延迟反馈技术对随机混沌控制也是十分有效的.关键词：随机Duffing系统延迟反馈控制随机混沌Gegenbauer多项式

Stochastic chaos in stochastic Duffing systems and its control by delayed feedback

The problem of stochastic chaos and its control by delayed feedback in a Duffing system with bounded random parameters (a stochastic Duffing system in short) under harmonic excitations is considered in detail. At first, the stochastic Duffing system is transformed into its equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation. Thus, the problem of chaotic response and its control in stochastic Duffing system can be reduced to that in an equivalent deterministic system. So the available effective mathematical methods and control strategies can be applied to the latter. Then, the main feature of stochastic chaos is fully explored, where the top Lyapunov exponent of the equivalent system obtained by Wolf's algorithm is used to identify the dynamic behavior of stochastic Duffing system. Finally, the control strategy of delayed feedback is applied to suppress or to induce chaotic response in the system. The results of numerical simulation show that by proper choice of feedback intensity and time delay, either suppressing or inducing stochastic chaos can be achieved. Hence, the strategy of delayed feedback control is also effective to stochastic chaos.