Spatiotemporal Organization of Chemical Oscillators via Phase Separation

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We develop a method for studying chemical oscillators in the presence of phase separation. Specifically, we define a dynamics at phase equilibrium by imposing timescale separation between slow reactions and fast diffusion. We show that colocalization of components can alter oscillator frequency and amplitude, and that it determines the stability of oscillations and fixed points. Although our method applies to general reaction networks with phase separation, we illustrate it on a concrete example of a three-component oscillator (“rock-paper-scissors” model) with two-phase coexistence. The analysis is validated with a spatial model, where relaxing the timescale separation between reactions and diffusion leads to waves of phase equilibria at mesoscopic scales.