Coherent regimes of globally coupled dynamical systems

TL;DR

This paper introduces a method to describe the collective behavior of large populations of coupled dynamical systems with diversity, enabling analysis of coherence, bifurcations, and phenomena like oscillator death.

Contribution

It provides an approximate yet quantitative framework to analyze macroscopic dynamics in diverse, globally coupled systems, applicable to any population size within the coherence region.

Findings

Effective mean field description of collective regimes

Analysis of bifurcations leading to coherence transitions

Illustration with chaotic oscillators showing oscillator death

Abstract

The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to populations of any size and functional form in the region of coherence. It requires linear variation or a narrow distribution for the dispersed parameter. Although being an approximation, the method allows us to quantitatively study the collective regimes that arise as a result of diversity and coupling and to interpret the transitions among these regimes as bifurcations of the effective macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator death and the route to full locking are examined for chaotic oscillators with time scale mismatch.