A Parallel Algorithm for Approximating One Dimensional Unstable Manifold of Discrete Dynamical Systems

Abstract

This paper presents a parallel algorithm for computing one dimensional unstable manifold of a hyperbolic fixed point of discrete dynamical system. It is pointed out that parallel computing can be realized by subdividing the unstable manifold into mutually independent subsections. In each subsection, the one dimensional unstable manifold is grown by forward iteration. Curvature constraint and distance control technique are applied to ensure the accuracy of the algorithm. An easy-to-implement recursive program is proposed for the interpolation of points. The simulation result shows that parallel computation is very accurate as well as efficient.