基于自适应因子轨道延拓法的不变流形计算

Computation of invariant manifolds with self-adaptive parameter and trajectories continuation method

提出自适应因子和轨道延拓相结合的二维流形计算方法,利用以平衡点为中心的椭圆对局域流形的近似,通过轨道的等距延拓和椭圆初始点的自适应调节,在精度要求下自适应的添加轨道,完成二维双曲不变流形的计算.此方法比"轨道弧长法"精度高,包含更多细节信息;同时要比"盒子细分法"更能反映流形的延拓趋势.

Most work on manifold study focuses on two-dimensional manifolds and there have been proposed some good computing methods.However,the computation of two-dimensional manifold is still a hot research field.In this paper the two-dimensional manifold of hyperbolic equilibria for vector fields is computed by combining self-adaptive parameter with trajectories continuation,approximating the local manifold with an ellipse around the equilibria,extending the trajectory with equal distance,and adjusting the trajectory with self-adaptive parameter.This method is more accurate than the ＂trajectories and arc-length method＂,and better shows the trend of the manifolds than the＂box covering method＂.