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We study the dynamics of phase synchronization in growing populations ofdiscrete phase oscillatory systems when the division process is coupled to thedistribution of oscillator phases. Using mean field theory, linear stabilityanalysis, and numerical simulations, we demonstrate that coupling betweenpopulation growth and synchrony can lead to a wide range of dynamical behavior,including extinction of synchronized oscillations, the emergence ofasynchronous states with unequal state (phase) distributions, bistabilitybetween oscillatory and asynchronous states or between two asynchronous states,a switch between continuous (supercritical) and discontinuous (subcritical)transitions, and modulation of the frequency of bulk oscillations.

Synchronization and phase redistribution in self-replicating populations of coupled oscillators and excitable elements