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A novel generalization of the Winfree model of globally coupled phaseoscillators, representing phase reduction under finite coupling, is studiedanalytically. We consider interactions through a non-infinitesimal (or finite)phase-response curve (PRC), in contrast to the infinitesimal PRC of theoriginal model. For a family of non-infinitesimal PRCs, the global dynamics iscaptured by one complex-valued ordinary differential equation resorting to theOtt-Antonsen ansatz. The phase diagrams are thereupon obtained for fourillustrative cases of non-infinitesimal PRC. Bistability between collectivesynchronization and full desynchronization is observed in all cases.

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