2021 Volume 13 Pages 40-43
A method of computing combinatorial Morse decomposition for a system of ordinary differential equations is proposed. It uses numerical solutions by Runge-Kutta method, and it is based on an affine approximation and QR decomposition. In contrast to interval arithmetic, it enables us to compute Morse decomposition at lower computational costs sacrificing for mathematical rigor. Numerical examples for time-T map of 3D ODE and a 3D Poincaré map for 4D ODE are presented for comparison between existing and proposed methods.
