【作者】 张莹； 徐伟； 方同；

【Author】 Zhang Ying1+ Xu Wei1 Tong Fang2 Hongxian Zhou1 1(Department of applied Mathematics, Northwestern Polytechnical University, Xi’an 710072) 2 (Department of Engineering Mechanics, Northwestern Polytechnical University, Xian 710072)

【机构】 西北工业大学应用数学系； 西北工业大学工程力学系；

【摘要】 本文首先运用Chebyshev多项式逼近的方法将具有有界随机参数的双势井Duffing-van der Pol系统转化为等价的确定性系统,继而研究其随机混沌现象,并利用噪声对其进行控制。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。数值结果表明,随机Duffing-Van der Pol系统的随机混沌现象与相应的确定性Duffing-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,同时在随机参数及其强度的影响下也呈现出一些特点。更多还原

【Abstract】 The stochastic Double-Well Duffing-van der Pol system with bounded random parameter is first transformed into an equivalent deterministic system by the Chebyshev polynomial approximation method, and then the stochastic chaos and its control by noise are investigated. Therefore the problem of controlling stochastic chaos in the stochastic Duffing-Van der Pol system can be reduced into the problem of controlling deterministic chaos in the equivalent system. The numerical simulations show that the chaos behavior in the stochastic Duffing-Van der Pol system is by and large similar to that in the equivalent deterministic Duffing-Van der Pol system. The chaos behavior can be controlled to the period states by noise, and with the effect of the random parameter and its intensity, there are still some features.更多还原