Secondary Poincaré section for characterizing dynamical behaviours of nonlinear systems

Zhengyuan Zhang and Liming Dai

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

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.

Keywords: Secondary Poincaré section; Nonlinear dynamical characteristics; Chaos; Quasiperiodicity; Poincaré map (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925008628

DOI: 10.1016/j.chaos.2025.116849

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