Canard phenomenon and localization of oscillations in the Belousov–Zhabotinsky reaction with global feedback

The occurrence of spatial domains of large amplitude oscillation on a background of small amplitude oscillation in a reaction–diffusion system is called localization. We study, analytically and numerically, the mechanism of localization in a model of the Belousov–Zhabotinsky reaction subject to glob...

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Published inThe Journal of chemical physics Vol. 119; no. 17; pp. 8824 - 8832
Main Authors Rotstein, Horacio G., Kopell, Nancy, Zhabotinsky, Anatol M., Epstein, Irving R.
Format Journal Article
LanguageEnglish
Published 01.11.2003
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ISSN0021-9606
1089-7690
DOI10.1063/1.1614752

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Summary:The occurrence of spatial domains of large amplitude oscillation on a background of small amplitude oscillation in a reaction–diffusion system is called localization. We study, analytically and numerically, the mechanism of localization in a model of the Belousov–Zhabotinsky reaction subject to global feedback. This behavior is found to arise from the canard phenomenon, in which a limit cycle suddenly undergoes a significant change in amplitude as a bifurcation parameter, in this case the feedback strength, is varied. In the system studied here, the oscillations arise via a supercritical Hopf bifurcation, but our analysis suggests that the same mechanism is relevant for systems undergoing a subcritical Hopf bifurcation.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.1614752