Dynamical systems with time-dependent coupling: Clustering and critical behaviour

TL;DR

This paper investigates how time-dependent interactions among motile elements lead to diverse collective behaviors, including clustering and phase transitions, with analytical insights in the large interaction range limit.

Contribution

It introduces a model of coupled motile elements with time-varying interactions driven by internal dynamics, revealing new dynamical regimes and a transition between order and disorder.

Findings

Identification of different dynamical regimes including clustering and disordered states.

Analytical treatment of the large interaction range limit as coupled phase oscillators.

Discovery of a transition between ordered and disordered collective behavior.

Abstract

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with autonomous dynamics. The system exhibits different dynamical regimes, with various forms of collective organization, controlled by the range of interactions and the dispersion of time scales in the evolution of the internal variables. In the limit of large interaction ranges, it reduces to an ensemble of coupled identical phase oscillators and, to some extent, admits to be treated analytically. We find and characterize a transition between ordered and disordered states, mediated by a regime of dynamical clustering.