  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.
