Coupling of identical chemical oscillators

Abstract

Identical BZ oscillators, in a CSTR, modeled by the Field-Koros-Noyes (FKN) mechanism, are coupled in a diffusion-like manner. In addition to the obvious symmetric solutions, i.e. solutions in which both CSTRs are oscillating in unison, or are in the same stable steady state, unsymmetric, broken symmetry, solutions may coexist under the same set of constraints. Thus, depending on constraints and initial conditions, the combined system can be in the following states: a) stable symmetric steady state. b) symmetric oscillations, when both cells oscillate in phase. c) coexistence of symmetric and unsymmetric steady states. d) coexistence of symmetric oscillations and unsymmetric stable steady state (broken symmetry). e) coexistence of symmetric and unsymmetric oscillations. The latter differ from the former in phase, in amplitude and in period. On the other hand, no unsymmetric oscillations were found to coexist with the symmetric steady state. All the initial conditions tried ended in either of the two, possible, stable states. The change of periods and amplitude of both types of oscillations are examined as a function of the system constraints namely, concentrations and coupling rate.