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

TL;DR

This paper investigates how population growth coupled with phase dynamics affects synchronization in oscillatory systems, revealing complex behaviors like bistability, phase redistribution, and transition types through theoretical and numerical analysis.

Contribution

It introduces a mean field framework to analyze phase synchronization in growing populations, uncovering novel dynamical regimes and transition phenomena not previously characterized.

Findings

Coupling growth and phase distribution can suppress or promote synchronization.

Multiple stable states including synchronized and asynchronous regimes are identified.

Transitions between states can be continuous or discontinuous depending on parameters.

Abstract

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.