  We study the dynamics of phase synchronization in growing populations of
discrete phase oscillatory systems when the division process is coupled to the
distribution of oscillator phases. Using mean field theory, linear stability
analysis, and numerical simulations, we demonstrate that coupling between
population growth and synchrony can lead to a wide range of dynamical behavior,
including extinction of synchronized oscillations, the emergence of
asynchronous states with unequal state (phase) distributions, bistability
between 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.
