随机Bonhoeffer-Van der Pol系统的随机混沌控制

讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象，并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道，但是在随机参数及其强度的影响下也呈现出一些特点.

Stochastic chaos and its control in the stochastic Bonhoeffer-Van der Pol system

In this paper, the stochastic chaos of the stochastic Bonhoeffer-Van der Pol system with bounded random parameter and its control by noise are investigated. The stochastic Bonhoeffer-Van der Pol system is first transformed into an equivalent deterministic system using the Chebyshev polynomial approximation, so that the problem of controlling stochastic chaos is reduced to the problem of controlling deterministic chaos in the equivalent system. Thus, the top Lyapunov exponent of the equivalent system can be used to examine the chaotic behavior and its control of the responses. The numerical simulations show that the chaos behavior in the stochastic Bonhoeffer-Van der Pol system is by and large similar to that in the equivalent deterministic Bonhoeffer-Van der Pol system. The chaos behavior can be controlled to the periodic states by noise, but under the effect of the random parameter and its intensity, it has cortain specific features.