Large Populations of Coupled Chemical Oscillators

TLDR: 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.