On stability and uniqueness of stationary one-dimensional patterns in the Belousov-Zhabotinsky reaction

Forbes L.K. (1991) On stability and uniqueness of stationary one-dimensional patterns in the Belousov-Zhabotinsky reaction. Physica D: Nonlinear Phenomena, 50 1: 42-58. doi:10.1016/0167-2789(91)90077-M


Author Forbes L.K.
Title On stability and uniqueness of stationary one-dimensional patterns in the Belousov-Zhabotinsky reaction
Journal name Physica D: Nonlinear Phenomena   Check publisher's open access policy
ISSN 0167-2789
Publication date 1991-01-01
Sub-type Article (original research)
DOI 10.1016/0167-2789(91)90077-M
Open Access Status Not Open Access
Volume 50
Issue 1
Start page 42
End page 58
Total pages 17
Subject 2604 Applied Mathematics
3109 Statistical and Nonlinear Physics
Abstract In this paper, a numerical solution technique is presented for obtaining time-independent spatial patterns of chemical concentration in the Belousov-Zhabotinsky reaction. The Oregonator model of the reaction is assumed, and the concentrations of each of the three principal intermediate species are expressed as Fourier series in the spatial variable, and the coefficients are then obtained by a straightforward Galerkin technique. Results of extensive numerical calculation are discussed, and it is demonstrated that, in many instances, the spatial pattern obtained is not unique, in the sense that at least two different patterns could be produced at the same values of the chemical rate constants and diffusion coefficients. The problem of whether the steady patterns are stable in time to small perturbations is discussed in detail. A criterion for stability of patterns of infinitesimal amplitude is established, and it is shown that, when all the diffusion coefficients are equal, there can be no stable small-amplitude solutions. However in the non-linear case, large-amplitude "quasi-stable" patterns have been discovered and these are discussed.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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