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

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.