具有随机参数的分数阶非线性系统的动力学及控制研究

项目名称： 具有随机参数的分数阶非线性系统的动力学及控制研究

项目编号： No.11302171

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 张莹

作者单位： 西北工业大学

项目金额： 26万元

中文摘要： 在非线性动力学的研究领域中，分数阶系统和随机现象已成为近年来的学术热点。目前，关于分数阶系统的研究大部分集中于确定性系统，而现实中很多分数阶系统存在随机特性，因此，同时考虑分数阶和随机问题将使系统更贴近实际。本项目以具有随机参数的分数阶非线性动力系统为对象，结合混沌多项式逼近理论、分数阶动力系统分析方法和现代控制理论，探索出一套理论和数值方法；借助全局分析策略，研究此类系统丰富的动力学现象，如分岔、混沌及其激变、共存吸引子和其吸引域，以及多种动力学行为的转化机理；将其结论与确定性和整数阶情形相比较，明确随机因素对系统行为的影响；针对倍周期分岔、Hopf分岔和混沌等运动，根据不同控制目标，综合考虑随机参数对系统动力学行为及控制的影响，特别是在分岔点和混沌激变处的作用，发展和设计一套控制方法，以期得到更切合实际且稳定的随机控制策略。

中文关键词： 随机非线性动力学；分数阶；随机参数；分岔；混沌

英文摘要： Recently, researches on fractional order system and stochastic phenomena have become the hot topics in the field of nonlinear dynamics. Up to now, the study on fractional order systems is mainly conducted for the deterministic systems, while there're a lot of fractional order systems have the stochastic features. It will be close to reality by studying on both of fractional order and stochastic problems. Based on the polynomial chaos theory, some matured research methods for fractional order dynamical systems, and the modern control theory, our program is aimed to exploring some theoretical and numerical methods for studying the nonlinear fractional order dynamical systems with random parameter. Using the global analysis, plenty of nonlinear phenomena in this kind of systems, such as bifurcations, chaos and crisis, coexist attractors and their basins, and the transforms between different motions are exhibited. Then, comparison between the obtained results with the phenomena in the deterministic system and integer order systems, illustrates the influence for the dynamical behaviors of the random parameter. In order to get the better and more stable control strategies, based on the different aims of control, considering the effect of the random parameter to the dynamical behaviors and control, especially around th

英文关键词： stochastic nonlinear dynamics；fractional order；random parameter；bifurcation；chaos