Collective periodicity in mean-field models of cooperative behavior

TL;DR

This paper demonstrates that adding dissipation to mean-field models of cooperative behavior can induce periodic orbits, especially when the reversible model undergoes a ferromagnetic phase transition, revealing new dynamical phenomena.

Contribution

It introduces a method to break symmetry in stochastic mean-field models and shows that dissipation leads to periodic orbits in the thermodynamic limit during phase transitions.

Findings

Dissipation induces periodic orbits in mean-field models.

Periodic behavior emerges during ferromagnetic phase transitions.

Symmetry breaking via dissipation affects collective dynamics.

Abstract

We propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.