The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory

TL;DR

This paper extends the Winfree model to include finite phase-response curves, using Ott-Antonsen theory to analyze the resulting dynamics and identify bistability phenomena.

Contribution

It introduces a generalized Winfree model with non-infinitesimal PRCs and derives a reduced ODE for global dynamics using Ott-Antonsen theory.

Findings

Bistability between synchronization and desynchronization observed.

Global dynamics captured by a single complex ODE.

Phase diagrams constructed for four PRC cases.

Abstract

A novel generalization of the Winfree model of globally coupled phase oscillators, representing phase reduction under finite coupling, is studied analytically. We consider interactions through a non-infinitesimal (or finite) phase-response curve (PRC), in contrast to the infinitesimal PRC of the original model. For a family of non-infinitesimal PRCs, the global dynamics is captured by one complex-valued ordinary differential equation resorting to the Ott-Antonsen ansatz. The phase diagrams are thereupon obtained for four illustrative cases of non-infinitesimal PRC. Bistability between collective synchronization and full desynchronization is observed in all cases.