Numerical Analysis of Bifurcation Problems

分岔问题的数值分析

• 批准号: 4274-2012
• 负责人: Doedel, Eusebius
• 金额: $ 3.06万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=513165
• 关键词: Numerical; Analysis; Bifurcation; Problems

My main research interest is the development, analysis, implementation, and application of numerical methods for analyzing the solution behavior of dynamical systems. My work is motivated by the fascinating changes of behavior exhibited by solutions to such equations as parameters are varied: there is tremendous satisfaction in devising new numerical algorithms that help increase our understanding of these phenomena. My recent research includes the determination of so-called invariant manifolds in the famous Lorenz equations, and especially the topological changes of these manifolds as parameter values enter the chaotic regime. Another study concerns the determination of stable and unstable manifolds of periodic orbits in the circular restricted 3-body problem, as these are of great current interest in the design of low-cost orbit transfers in space mission design. Also of practical interest is the analysis of laser models, several of which predict the qualitative and even quantitative behavior of actual physical experiments very well.

我的主要研究兴趣是发展，分析，实施和应用数值方法来分析动力系统的解决方案的行为。我的工作是由迷人的行为变化所表现出的解决方案，如参数不同的方程：有巨大的满足设计新的数值算法，有助于提高我们对这些现象的理解。我最近的研究包括著名的洛伦兹方程中所谓的不变流形的确定，特别是这些流形的拓扑变化作为参数值进入混沌状态。另一项研究涉及在圆形限制性三体问题中确定周期轨道的稳定和不稳定流形，因为这些在空间使命设计中的低成本轨道转移设计中具有重要意义。激光模型的分析也具有实际意义，其中有几个模型可以很好地预测实际物理实验的定性甚至定量行为。