Canard explosion and excitation in a model of the Belousov-Zhabotinsky reaction

Morten Brøns, Kedma Bar-Eli

Research output: Contribution to journalArticlepeer-review

Abstract

The experimental evidence for sudden formation of relaxation oscillations (hard transitions), or the sudden change of amplitude and period of oscillations, is reviewed. It is shown that, in addition to the well-known mechanisms for hard transitions, there is another way in which a very fast transition from small to large oscillations can occur. This mechanism termed canard explosion is analyzed in terms of a well-known chemical model, the two-variable Oregonator. The theory of the canard explosion, which occurs close to a Hopf bifurcation, is analyzed and compared with computational results. The resulting difficulties of differentiating experimentally among the various transition mechanisms are discussed. The well-known phenomenon of excitation, i.e., a large deviation of a system (chemical, neural, or other) after perturbation from a stable steady state, is shown to be closely related to the canard explosion. The common mathematical properties of the system, on which both phenomena depend, are discussed.

Original languageEnglish
Pages (from-to)8706-8713
Number of pages8
JournalJournal of Physical Chemistry
Volume95
Issue number22
DOIs
StatePublished - 1991

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