随机Duffing映射的Charlier多项式逼近与分岔研究

摘要

Dynamical behaviors and stochastic bifurcation of Duffing map are investigated under the random parameters by Charlier polynomial approximation method.In order to clarify the stochastic characteristic of Duffing map,the complex dynamical behaviors of deterministic Duffing map are explored,especially about generation,evaluation and transformation of the dynamical motions.Then,according to the type of random parameters,the corresponding Charlier orthogonal polynomial is applied to achieve the approximation of stochastic Duffing map,which is its extended order equivalent deterministic system,and the ensemble average responses of this equivalent system can be applied to analyze the stochastic bifurcation behaviors.The numerical simulation results show that under the effect of stochastic factors,the periodic bifurcation points move forward,and the convergence parameter interval is shrinking with the increasing random variable intensity.%在参数随机性影响下,借助Charlier正交多项式逼近,实现了Duffing映射系统的动力学行为和随机分岔研究.为了明确系统的随机特性,首先,对确定性Duffing映射的复杂动力学行为进行分析,明确其动力学行为的发生、发展和变化规律;其次,针对系统随机参数的类型,选取相应的Charlier正交多项式实现对随机Duffing映射的逼近,得到扩阶等价确定性系统,进而运用集合平均响应实现随机分岔行为分析.数值结果表明,受随机因素的影响,倍周期分岔点发生前移;且系统的收敛区域随着随机变量强度的增加而缩小.