Approximate solution for the oscillation death state in pulse coupled oscillators

TL;DR

This paper investigates the oscillation death state in pulse coupled phase oscillators, revealing that phase behavior depends mainly on inverse degree and is influenced by degree-frequency correlation, with analytical approximations supporting numerical findings.

Contribution

It provides a simple analytical approximation for the oscillation death state, highlighting the role of network topology and degree-frequency correlation in pulse coupled oscillators.

Findings

Phases depend primarily on inverse degree.

Degree-frequency correlation inhibits oscillation death.

Analytical approximations align with numerical results.

Abstract

We study numerically the oscillation death state in the phase oscillator model proposed byWinfree. We found that the phases in this state follow very simple rules, actually, besides intrinsic properties of the oscillators, such as natural frequency and pulse shape, they depend only on the inverse of the degree. Other topological properties such as transitivity or associativity seems to play no role on this state. Furthermore, we found that degree-frequency correlation helps to inhibit oscillation death. Simple analytical approximations corroborate the numerical results.