含有约束的两个状态变量系统的转迁集计算  

Transition Sets of Bifurcations of Dynamical System With Two State Variables With Constraints

作　　者：李军[1] 陈予恕[1] 

机构地区：[1]哈尔滨工业大学航天学院137信箱,哈尔滨150001

出　　处：《应用数学和力学》2012年第2期135-152,共18页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10632040)

摘　　要：周期解的分岔广泛存在于实际的非线性动力学系统中.该文对两个状态变量系统的约束分岔进行了讨论.在约束条件下系统将产生新的转迁集.此外,以一个二维系统为例,对含有约束条件和不含有约束条件的分岔特性进行了比较.所得的结果可以为系统的设计和参数选择提供理论依据.Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. Cate- gories of bifurcations of systems with two state variables with different types of constraints were discussed where some new types of transition sets were added. Additionally, the bifurca- tion properties of two-dimensional systems without constraints were compared with the ones with constraints. The results obtained can be used by engineers for the choice of the structural parameters of the system.

关 键 词：分岔 约束 奇异性理论 非线性动力学 两状态变量 

分 类 号：O322[理学—一般力学与力学基础] TH133[理学—力学]