随机Duffing映射的Charlier多项式逼近与分岔研究

发布时间：2018-10-24 22:52

【摘要】：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。
[Abstract]:Under the influence of parameter randomness, the dynamic behavior and stochastic bifurcation of Duffing mapping system are studied by means of Charlier orthogonal polynomial approximation. In order to clarify the stochastic characteristics of the system, firstly, the complex dynamic behavior of deterministic Duffing mapping is analyzed, and the occurrence, development and variation of the dynamic behavior are clarified. Secondly, the types of random parameters of the system are analyzed. The corresponding Charlier orthogonal polynomials are selected to approximate the stochastic Duffing maps, and the extended equivalent deterministic systems are obtained, and then the stochastic bifurcation behavior analysis is realized by means of the set average response. The numerical results show that the bifurcation point of doubling period moves forward under the influence of random factors, and the convergence region of the system shrinks with the increase of the strength of random variables.
【作者单位】：西北工业大学理学院;西北工业大学力学与土木建筑学院;
【基金】：国家自然科学基金项目(11302171,11672232) 陕西省自然科学基础研究计划资助项目(2016JQ1015)资助
【分类号】：O174.41

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