Analytical approximation of a self-oscillatory reaction system using the Laplace-Borel transform

Chi Zhai and Wei Sun

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: Time-symmetry breaking bifurcations cause an open system to generate complex structures/patterns, prompting the study of far-from-equilibrium and nonlinear thermodynamics. Specifically, thegeneration of self-organized chemical-wave patterns by the Belousov-Zhabotinsky reaction attractedattention from the academic community, assimilar structureswidely exist in the chemical/biological environment. However, theoretical fundamentals of these self-oscillatory structures are yet to be adequately addressed. This paper introducesa frequency-domain method for approximating the Belousov-Zhabotinskyreaction system.The nonlinear dynamics of the oscillator is estimated using the Laplace-Borel transform, which is an extension of the Laplace transform andutilizesfunctional expansions to approximate the nonlinear terms in the dynamic system.The method is applied to theBelousov-Zhabotinskyreaction model to yieldamplitude, frequency and stability characteristics near theAndronov-Hopf bifurcation points. By studying the emergence of self-oscillatory patternsusing this analytical method, new insights towardsfar-from-equilibrium and nonlinearthermodynamics are explored.

Keywords: Nonlinear frequency analysis; Shuffle algebra; Far-from-equilibrium thermodynamics; The Belousov-Zhabotinsky reaction (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920309000

DOI: 10.1016/j.chaos.2020.110508

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