On the temporal characteristics of a model for the Zhabotinskii-Belousov reaction

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The number and stability of stationary and periodic solutions in a semi- phenomenological reaction mechanism that qualitatively models the Zhabotinskii- Belousov reaction are studied as functions of parameters in the model. Both multiple stationary solutions and multiple periodic solutions can exist simultaneously. Periodic solutions bifurcate in one of three ways: at zero amplitude as predicted from the Hopf theorem; pairwise at finite amplitude, the so-called "hard" bifurcation; or by coalescense with separatrix loops. Detailed computations for several cases reveal the dependence of the period and amplitude of the periodic solutions on the parameters. The results show that the model exhibits all the qualitative features that might be expected in intracellular reactions and so can serve as a model system for theoretical studies of pattern formation in developing systems.

Original languageEnglish (US)
Pages (from-to)205-238
Number of pages34
JournalMathematical Biosciences
Volume24
Issue number3-4
DOIs
StatePublished - 1975

Fingerprint Dive into the research topics of 'On the temporal characteristics of a model for the Zhabotinskii-Belousov reaction'. Together they form a unique fingerprint.

Cite this