Stability of traveling waves in the Belousov-Zhabotinskii reaction

David A. Kessler, Herbert Levine

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


It is well known that the Belousov-Zhabotinskii reaction can exhibit planar traveling waves in the excitable-kinetics regime. Using the previously formulated piecewise-linear Oregonator model, we study the stability of these waves to general disturbances. We find possible linear instabilities, either to transverse structure or to a longitudinal oscillation; these set in below a critical velocity, and which one occurs first depends on the ratio of the diffusivities of the two chemical species. We also consider the weakly nonlinear bifurcation analysis for the steady-state bifurcation, showing that the bifurcation is supercritical over a wide parameter range. The implications of these results for experimental systems are briefly discussed.

Original languageEnglish
Pages (from-to)5418-5430
Number of pages13
JournalPhysical Review A
Issue number10
StatePublished - 1990
Externally publishedYes


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