Exploring diverse trajectory patterns in nonlinear dynamic systems

Alžběta Lampartová and Marek Lampart

Chaos, Solitons & Fractals, 2024, vol. 182, issue C

Abstract: Describing the dynamical properties of explored systems, one finds the need to distinguish between various types of trajectories. The nature of trajectories is often split into regular and irregular, which will be shown in this paper as too crude. Hence, the main aim of this paper is to give a classification of trajectories reflecting persistence, regularity, chaos, intermittency, and transiency. To depict such phenomena, classical examples from discrete (the Rulkov map) and continuous (the Lorenz system) dynamical systems are applied. In these cases, the maximal Lyapunov exponent, the 0-1 test for chaos, the bifurcation diagram, and the Fourier analysis are applied, and these dynamics characteristics are confronted with trajectory types.

Keywords: Regular; Chaos; Transient; Intermittent; 0-1 test for chaos; Maximal Lyapunov exponent; Bifurcation diagram (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924004156

DOI: 10.1016/j.chaos.2024.114863

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