一般Clairaut型微分方程的多参数分支

Multi-parameter Bifurcations of Differential Equations of General Clairaut Type

一般Clairaut型微分方程是Clairaut微分方程的推广.本文利用Legendre开折理论与横截理论从几何学的角度对这类方程的多参数分支进行分类,并通过模拟对其中几类经典的相位图分支作出图像.结果可用于研究当参数改变时此类系统拓扑结构的变化.

General Clairaut type differential equations are the generalization of classical Clairaut differential equations.By applying the theories of Legendrian unfolding and transversality,the multi-parameter bifurcations of such differential equations are classified from the geometric point of view.And through the simulation,several typical bifurcation diagrams of the phase portraits are drawn.The results can be used to study the change of the system topology when the parameters are changed.