项目名称: 高维非线性动力学系统规范形计算及应用的研究
项目编号: No.11302184
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: 陈淑萍
作者单位: 厦门理工学院
项目金额: 21万元
中文摘要: 力学、航空航天和机械工程领域中,许多问题的力学模型可用高维非线性系统来描述。规范形理论是研究动力系统、微分方程及非线性振动等领域动力学特征的强有力工具,对于分叉和混沌动力学的研究具有重要的理论意义和深远的影响。由于高维系统可以更为准确地模拟工程问题,因此,发展计算高维非线性系统最简规范形的方法是非常重要和迫切的。本项目拟通过理论分析和数值模拟相结合的方法研究高维非线性系统的动力学,提出计算高维非线性系统最简规范形的新方法。主要内容包括:利用重正化群理论和谱序列方法计算高维非线性系统的最简规范形;利用所提出的方法研究高维非线性系统的分叉与混沌动力学。
中文关键词: 规范形;分叉;稳定性;边界退化;非线性动力学
英文摘要: The mechanical models for a variety of problem in the field of mechanics, aircraft, aerospace, mechanical engineering, can be described by high-dimensional nonlinear systems. The normal form theory is one of the useful tools in the fields of dynamical system, ordinary differential equations and nonlinear vibration and stress a profound influence on complex dynamic theory such as bifurcation and chaos dynamics. In reality, the formulation of high-dimensional nonlinear systems can be used to describe realistic engineering problems mathematically, the development of new computation methods to refine the normal forms for high dimensional nonlinear systems is indispensable.This project presents the renormalization group theory and the method of spectral sequences, which are used for the search of normal forms for large classes of high-dimensional nonlinear systems. Furthermore, the complex behavior patterns of nonlinear systems, such as bifurcation and instability will also be investigated.
英文关键词: Normal form;Bifurcation;Stability;Boundary degeneracy;Nonlinear dynamics