Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

TL;DR

This paper investigates how positive correlations between natural frequencies and coupling strengths influence the collective dynamics of mixed populations of excitable and oscillatory units, revealing conditions for excitable behavior emergence.

Contribution

It introduces a mean-field approach combined with a Gaussian approximation to analyze the impact of frequency-coupling correlations in coupled active rotator populations.

Findings

Excitable behavior requires excitable elements to have smaller coupling strengths.

Positive frequency-coupling correlations shape the global dynamics.

Reduced equations capture complex population behaviors.

Abstract

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.