Journal ArticleDOI
Large Populations of Coupled Chemical Oscillators
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In this paper, the authors study the mechanisms that underlie synchronization processes in large systems of coupled chemical oscillators and derive a nonlinear integro-differential equation that describes how the distribution of the oscillators' phases evolves in time.Abstract:
We study the mechanisms that underlie synchronization processes in large systems of coupled chemical oscillators. By synchronization, we mean the evolution from an initial state where the phases of the oscillators are distributed randomly, to a final state where all the oscillators are in phase. In the continuum limit, where there are many oscillators per unit volume, we derive a nonlinear integro-differential equation that describes how the distribution of the oscillators’ phases evolves in time. In general, this problem is very formidable. But we discover some important special cases for which there are exact solutions describing synchronization processes.read more
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References
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Journal ArticleDOI
Synchronization in two interacting oscillatory systems.
Miloš Marek,Ivan Stuchl +1 more
TL;DR: Nonlinear phenomena arising from the interaction of two oscillating systems of chemical reactions are studied experimentally, and mathematical modelling of the above phenomena failed, probably due to insufficient knowledge of a kinetic model.
Journal ArticleDOI
Coupled Chemical Oscillators
TL;DR: In this article, the interaction between a pair of coupled chemical oscillators was analyzed using singular perturbation techniques, and an equation that governs the time evolution of the phase shift was derived, which is a measure of how much the oscillators are out of phase.