An ensemble of pulse-coupled phase oscillators is thoroughly analyzed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is observed. The “synchronized” phase, which emerges upon increasing the coupling strength, is characterized by highly irregular fluctuations: A time-series analysis reveals that the dynamics of the order parameter is indeed high dimensional. The complex dynamics appears to be the result of the nonperturbative action of a suitably shaped phase-response curve. Such a mechanism differs from the often-invoked balance between excitation and inhibition and might provide an alternative basis to account for the self-sustained brain activity in the resting state. The potential interest of this dynamical regime is further strengthened by its (microscopic) linear stability, which makes it quite suited for computational tasks. The overall study has been performed by combining analytical and numerical studies, starting from the linear stability analysis of the asynchronous regime, to include the Fourier analysis of the Kuramoto order parameter, the computation of various types of Lyapunov exponents, and a microscopic study of the interspike intervals.
A.P. wishes to acknowledge a discussion with M. Wolfrum on the stability of the Kuramoto model. This work is partially supported by the ITN-EJD COSMOS (No. 642563) project.
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics