关键词: 动力系统, 不变流形, 双曲, 洛伦兹流形

Abstract: The computation of manifold plays an important role in understanding the dynamics of a nonlinear system. This paper presented a revised algorithm for computing two dimensional manifolds of vector fields. The trajectory was grown by solving appropriate initial value problem, then the manifold was grown step by step with equal arc-length along the trajectory and points on the trajectory were selected according to the local curvature. For the first time, both curvature-control technique and distance constraints were employed when interpolation between mesh points was needed. And in this way, the accuracy of interpolated points was guaranteed and it was the main advantage over the existing methods. The simulation results show that the proposed algorithm is effective.

Key words: dynamical system, invariant manifold, hyperbolic, Lorenz manifold