Bifurcation theory and applications

分岔理论及应用

• 批准号: 8329-2007
• 负责人: Langford, William
• 金额: $ 1.09万
• 依托单位: University of Guelph
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=420596
• 关键词: Bifurcation; theory; applications

In the study of systems of mathematical equations, Bifurcation Theory explains how small changes in the parameters of the equations can lead to disproportionate changes in the solutions of the equations. Bifurcation Theory tells us that this "cause and effect" relationship is not arbitrary, but is most likely to occur only in a few typical (or generic) ways, called bifurcations, which mathematicians are beginning to understand fairly well. In the present work, the equations under study are nonlinear systems of differential equations; that is, equations that determine how a system evolves with time. Equations of this kind are widely used in science, and help in the understanding of many kinds of real systems, for example in physics, engineering and biology.

在对数学方程式系统的研究中，分叉理论解释了方程参数的小变化如何导致方程解的不成比例的变化。 分叉理论告诉我们，这种“因果关系”的关系不是任意的，但最有可能仅以少数典型（或通用的）方式发生，称为分叉，而数学家开始很好地理解这些关系。 在目前的工作中，所研究的方程是微分方程的非线性系统。 也就是说，确定系统如何随时间发展的方程式。 这种方程式在科学中广泛使用，并有助于理解许多实际系统，例如物理，工程和生物学。