非线性系统周期解的单调同伦方法

MONOTONE HOMOTOPY METHODS FOR PERIODIC SOLUTIONS OF NONLINEAR DYNAMICAL SYSTEMS

研究非线性动力系统周期解的单调同伦法。首先讨论周期解同伦的折叠奇异性。给出了周期解曲线出现折点的充要条件。提出数值求周期解的单调同伦方法，证明了它的全局收敛性。同时指出了它的二阶收敛性。最后给出数值例子。说明本方法的有效性。

This paper deals with the numerical periodic solutions of nonlinear dynamical systems. The fold point singularity of the homotopy of periodic solutions is discussed, and the sufficient and necessary condition for the fold point is also given. Then a novel monotone homotopy method is developed for solving the periodic solution and its global convergence is proved as well. Finally the effectiveness of this method is illustrated with a numerical example.