摘要
研究了含有两个分岔参数的多频激励下Duffing-van der Pol系统的分岔特性.分3种情况进行了讨论:情形1,将λ1看成分岔参数;情形2,将λ2看成分岔参数;情形3,将λ1和λ2都看成分岔参数.根据转迁集的定义,不同的情况下,整个参数空间都被分成了若干个不同的区域,得到了各个参数空间上系统的分岔图,从而为该类系统的参数优化控制奠定了基础.
Bifurcation properties of Duffing-van der Pol System with two parameters under multi-frequency excitations were studied. It was discussed for three cases： 1 λ1 was considered as bifurcation parameter,2 λ2 was considered as bifurcation parameter,3 λ1 and λ2were both considered as bifurcation parameters. According to the definition of transition sets,the whole parametric space was divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions were obtained,which could provide a theoretical basis for optimal design of the system.
出处
《应用数学和力学》
CSCD
北大核心
2010年第8期971-978,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金(重点)资助项目(10632040)
