Movement Characteristics of a Model with Circular Equilibrium

Lampart, Marek; Nagyová, Judita Buchlovská

doi:10.1007/978-3-030-35441-1_5

Cited by 2 publications

(1 citation statement)

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“…The results return values close to either 0 or 1, with 0 corresponding to regular dynamics and 1 to chaotic dynamics. With its easy implementation, evaluation, and wide range of application, using this tool for detecting chaos is becoming more popular in different fields [35][36][37][38] .…”

Section: Resultsmentioning

confidence: 99%

Detection of embedded dynamics in the Györgyi-Field model

Nagyová

Jansı́k

Lampart

2020

Sci Rep

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The main aim of this paper is to detect embedded dynamics of the Györgyi-Field model of the Belousov–Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, an analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques; namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0–1 test for chaos, approximate entropy, and the maximal Lyapunov exponent. The correlation between approximate entropy and the 0–1 test for chaos was observed and described in detail. The main discovery was that the three-stage system of nested sub-intervals of flow rates showed the same pattern in the 0–1 test for chaos and approximate entropy at every level. The investigation leads to the open problem of whether the set of flow rate parameters has Cantor-like structure.

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Section: Resultsmentioning

confidence: 99%