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

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.