Dynamics of a population of oscillatory and excitable elements

TL;DR

This paper analyzes a model of coupled oscillatory and excitable elements, revealing how coupling width and type influence system stability, bistability, and persistent activity through analytical bifurcation analysis.

Contribution

It introduces an analytical reduction of a complex population model to a two-dimensional system, elucidating the effects of coupling function shape on dynamics.

Findings

Broad coupling leads to bistability between high and low activity states.

Narrow inhibitory coupling can produce persistent pulsations.

Analytical bifurcation curves characterize stability regimes.

Abstract

We analyze a variant of a model proposed by Kuramoto, Shinomoto, and Sakaguchi for a large population of coupled oscillatory and excitable elements. Using the Ott-Antonsen ansatz, we reduce the behavior of the population to a two-dimensional dynamical system with three parameters. We present the stability diagram and calculate several of its bifurcation curves analytically, for both excitatory and inhibitory coupling. Our main result is that when the coupling function is broad, the system can display bistability between steady states of constant high and low activity, whereas when the coupling function is narrow and inhibitory, one of the states in the bistable regime can show persistent pulsations in activity.