Complex synchronization transitions in globally coupled excitable systems with noise-induced coherent oscillations

Noise can induce coherent oscillations in excitable systems without deterministic limit cycles. Though synchronization between a pair of such coherent excitable systems has been studied, collective synchronization transitions in large populations of coherent excitable systems remain yet to be uncovered. In this paper, collective synchronization dynamics of globally coupled coherent excitable systems exhibiting self-induced stochastic resonance are investigated. Five synchronization stages with distinct collective dynamics of different symmetries are revealed. The effective phase equation and corresponding nonlinear Fokker-Planck equation are established to reproduce the collective synchronization dynamics. By introducing the effect of phase-dependent noise, the full scenario of synchronization stages can be described. These results provide insight into the collective behaviors of noise-induced coherent oscillators in biological systems. Noise can induce ordered behaviors in excitable systems like climate models or neuronal systems, yet how these noise-induced oscillators interact in large populations remains elusive. This study shows that complex synchronization transitions can be observed in globally coupled excitable units exhibiting noise-induced coherent oscillations.