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An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in thepresence of a mean-field coupling and a dispersion of their naturalfrequencies. In spite of the analogies with the Kuramoto setup, a much richerscenario is observed. The "synchronised phase", which emerges upon increasingthe coupling strength, is characterized by highly-irregular fluctuations: atime-series analysis reveals that the dynamics of the order parameter is indeedhigh-dimensional. The complex dynamics appears to be the result of thenon-perturbative action of a suitably shaped phase-response curve. Suchmechanism differs from the often invoked balance between excitation andinhibition and might provide an alternative basis to account for theself-sustained brain activity in the resting state. The potential interest ofthis dynamical regime is further strengthened by its (microscopic) linearstability, which makes it quite suited for computational tasks. The overallstudy has been performed by combining analytical and numerical studies,starting from the linear stability analysis of the asynchronous regime, toinclude the Fourier analysis of the Kuramoto order parameter, the computationof various types of Lyapunov exponents, and a microscopic study of theinter-spike intervals.

Self-sustained irregular activity in an ensemble of neural oscillators