Secondary Poincaré section for characterizing dynamical behaviours of nonlinear systems

Abstract

An innovative secondary Poincaré section method is presented in this research to characterize the behaviours of nonlinear dynamical systems, especially quasiperiodicity and chaos. To circumvent the difficulty of computing the intersection between a discrete point set and a plane, a closed curve is iteratively mapped to approach the Poincaré attractor. In this way, the proposed method effectively defines a secondary Poincaré plot that is more accurate and rigorous than existing methods. It lays the groundwork for dimensionality reduction analysis for nonlinear dynamical systems.