计算分岔规范型和普适开折的同调方法  

Homological Method on Computations of Bifurcation Normal Form and Universal Unfolding

作　　者：彭国俊[1] 陈潮填[1] 

机构地区：[1]广东技术师范学院计算机科学学院,广州510665

出　　处：《吉林大学学报（理学版）》2013年第5期783-788,共6页Journal of Jilin University:Science Edition

基　　金：广东省自然科学基金(批准号:s2012040006688);广东省教育厅科技创新项目(批准号:2012KJCX0073)

摘　　要：应用同调方法研究分岔规范型和普适开折的显式计算.对于Z2对称的double-zero分岔,给出了同调方程,导出了规范型的显式计算公式,建立了计算普适开折的线性代数方程,并以一个修改的van der Pol系统为例,说明了该方法在分岔分析上的优势.We investigated the computations of bifurcation normal form and universal unfolding with the homological method. For the double-zero bifurcation with Z2-symmetry, we gave the homological equation, and derived the explicit computational formulae of normal form, and constructed the linear algebra equations for universal unfolding. Finally, we took a modified van der Pol system as an example to show the advantages of this method.

关 键 词：double—zero分岔 规范型 普适开折 同调方法 

分 类 号：O175.14[理学—数学]