退化点上van der Pol-Mathieu方程分叉解的稳定性研究

The Stability of Bifurcation Solutions for van der Pol-Mathieu Equation on the Degenerate Points

研究了著名的 van der Pol-Mathieu方程 1 / 2次谐共振分叉在退化点的零解和极限环的稳定性问题 ,零解的稳定性用中心流形方法研究 ,Hopf分叉产生的极限环的稳定性用

Two of very important bifurcation problems of van der Pol Mathieu system are investigated in present paper.The stability of zero bifurcation solution at the degenerate points is studied with center manifold method,and the stability of limit cycle in the Hopf bifurcation is analyzed by means of Hopf bifurcation theorem.