Type-III intermittency in emergent bursting dynamics of globally coupled rotators

TL;DR

This paper investigates the transition to chaos in globally coupled rotators, revealing type-III intermittency through analysis of bursting dynamics and bifurcation scaling in a bimodal Kuramoto model.

Contribution

It demonstrates the occurrence of type-III intermittency in a mean-field model of coupled rotators, linking bursting dynamics to chaos transition mechanisms.

Findings

Identification of type-III intermittency in bursting oscillations.

Reconstruction of first-return maps for inter-burst intervals.

Scaling laws for laminar periods near the transition.

Abstract

Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the transition between these two regimes, where the dynamics consists of periods of nearly regular bursting interspersed with irregular spiking intervals, and demonstrate its correspondence to intermittent transition to chaos. Specifically, we consider a bimodal Kuramoto model with linear global feedback, which allows for a mean-field formulation of the dynamics and thus to investigate the phenomenology in the thermodynamic limit. We reconstruct the one-dimensional first-return maps of inter-burst intervals and estimate the Floquet multiplier associated with the unstable bursting solution. The results indicate type-III intermittency, which is also supported by the scaling of the average laminar periods as the control parameter varies, along with their probability density distribution.