Critical exponents of the transition from incoherence to partial oscillation death in theWinfree model

Abstract

We consider an analytically solvable version of the Winfree model of synchronization ofphase oscillators (proposed by Ariaratnam and Strogatz 2001 Phys. Rev. Lett. 86 4278). It isobtained that the transition from incoherence to a partial death state is characterized bythird-order or higher phase transitions according to the Ehrenfest classification.The order of the transition depends on the shape of the distribution function fornatural frequencies of oscillators in the vicinity of their lowest frequency. Thecorresponding critical exponents are found analytically and verified with numericalsimulations of equations of motion. We also consider the generalized Winfree modelwith the interaction strength proportional to a power of the Kuramoto orderparameter and find the domain where the critical exponent remains unchanged by thismodification.