Bogdanov-Takens系统极限环和同宿轨线及分岔  

Limit Cycles and Homoclinic Orbits and Their Bifurcation of the Bogdanov-Takens System

作　　者：黄赪彪[1] 刘佳[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275

出　　处：《应用数学和力学》2008年第9期1083-1088,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10672193)

摘　　要：讨论Bogdanov-Takens系统极限环、同宿轨线及其关于参数分岔的曲线定量分析.给出这些问题的近似解析表达式的参数增量法;利用时间变换,将极限环和同宿轨线表示为广义谐函数的解析表达式;画出参数与极限环关于振幅稳定性特征指数、极限环与同宿轨线的相图,以及参数的分岔图等曲线.The quantitative analysis of limit cycles and homoclinic orbits and the bifurcation curve for the Bogdanov-Takens system were discussed. The parameter incremental method for approximate analytical-expressions of these problems was given. These analytical-expressions of the limit cycle and homoclinic orbit were shown as the generalized harmonic function by employing a time transformation. Some curves for the parameters and the stability characteristic exponent of limit cycle versus amplitude were drawn. And some of the limit cycles and homoclinic orbits phase portraits were plotted. And the relationship curves of parameterand μ and λ with amplitude a and the bifurcation diagrams about the parameter were given too. The numerical accuracy of calculation results was good.

关 键 词：BOGDANOV-TAKENS系统 极限环 同宿轨线 分岔图 参数增量法 

分 类 号：O322[理学—一般力学与力学基础] V215.34[理学—力学]