项目名称: 非光滑高维非线性系统的全局分岔、混沌动力学及应用
项目编号: No.11472315
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 杨凤红
作者单位: 中央财经大学
项目金额: 82万元
中文摘要: 非光滑动力系统的非光滑分岔问题近年来倍受关注。本项目拟对非光滑高维非线性系统中涉及同宿轨和异宿轨等非光滑全局分岔、混沌动力学及应用问题进行研究。 目前有关非光滑动力系统的研究成果以系统的平衡点和周期解相关的局部分岔为主,而对于涉及同宿轨或异宿轨的,由非光滑特性诱导的全局分岔乃至混沌动力学方面的研究则较少。本项拟利用非线性分析方法和动力系统理论,研究非光滑高维非线性系统中同宿轨与异宿轨的存在性、参数变化时引起的同宿和异宿分岔,以及由此引起的混沌等复杂动力学行为;针对具有裂纹或干摩擦等非光滑因素的机械系统、经济与金融动力学中的经济增长和金融寡头等典型问题建立非光滑高维非线性动力学方程,讨论系统的非光滑全局分岔与混沌动力学特性,揭示系统蕴涵的复杂动力学现象。 本项研究将进一步发展非光滑分岔理论,并有着重要的应用价值。
中文关键词: 高维非线性系统;非光滑;全局分岔;混沌动力学
英文摘要: Nonsmooth bifurcations in nonsmooth dynamical systems have been paid more attentions in the last two decades. In this project, nonsmooth global bifurcations about homoclinic and heteroclinic orbits, chaotic dynamics in nonsmooth higher dimentional nonlinear systems and their applications will be studied. Now the literatures mainly focus on nonsmooth local bifurcations near equilibria or periodic orbits, however, the results on nonsmooth global bifurcations of homoclinic or heteroclinic orbits are lesser. Using the nonlinear analysis methods and dynamical system theory, we will study the existence of homoclinic and heteroclinic orbits in nonsmooth higher dimensional nonlinear dynamical systems, the homoclinic and heteroclinic bifurcations due to the parameters varying, and other complicated dynamical behaviors such as chaos;nonsmooth higher dimentional nonlinear dynamical equations will be established for mechanical sytems with crack or dry-friction and typical problems, such as economic growth and oligopoly model, in economy and finance. Then nonsmooth global bifurcation and chaotic dynamics will be discussed to show their intrinsic and complex dynamical behaviors. The study of the project will further develop the nonsmooth bifurcation theory that is significant in applications.
英文关键词: higher dimentional nonlinear system;nonsmooth;global bifurcation;chaotic dynamics