含约束非线性动力系统的分岔分类

基金项目: 国家自然科学基金资助项目(重大19990510);国家重点基础研究专项经费资助项目(G1998020316)

Classification of Bifurcations for Nonlinear Dynamical Problems With Constraints

摘要: 讨论含约束非线性动力系统分岔的分类.研究表明,约束分岔的转迁集,除分岔集、滞后集和双极限点集外,还有三种转迁集是它特有的.在此基础上提出了一种约束分岔问题的奇异性分类方法.
- 约束 /
- 分岔 /
- 奇异性 /
- 非线性动力系统
Abstract: Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed.All its six types of transition sets are derived,in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.
- constraint /
- bifurcation /
- singularity /
- nonlinear dynamical problem

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