Open AccessComputation of invariant manifolds with self-adaptive parameter and trajectories continuation method
Author(s) -
Meng Jia,
Yangyu Fan,
Huimin Li
Publication year - 2010
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.59.7686
Subject(s) - continuation , manifold (fluid mechanics) , computation , invariant manifold , stable manifold , invariant (physics) , trajectory , vector field , ellipse , computer science , numerical continuation , mathematics , center manifold , mathematical analysis , algorithm , geometry , physics , mathematical physics , programming language , mechanical engineering , hopf bifurcation , nonlinear system , astronomy , quantum mechanics , bifurcation , engineering
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".