机械科学与技术2017，Vol.36Issue(2)：190-195,6.DOI:10.13433/j.cnki.1003-8728.2017.0205
随机Duffing映射的Charlier多项式逼近与分岔研究
Bifurcation Analysis of Stochastic Duffing Map via Charlier Polynomial Approximation
摘要
Abstract
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.关键词
Duffing映射/随机参数/Charlier多项式/分岔/混沌Key words
Duffing map/random parameter/Charlier polynomial/bifurcation/chaos分类
数理科学引用本文复制引用
张莹,岳晓乐,都琳,王亮,方同..随机Duffing映射的Charlier多项式逼近与分岔研究[J].机械科学与技术,2017,36(2):190-195,6.基金项目
国家自然科学基金项目(11302171,11672232)与陕西省自然科学基础研究计划资助项目(2016JQ1015)资助 （11302171,11672232）
