The effect of pulse width on the dynamics of pulse-coupled oscillators

Neuronal networks with a nearly balanced excitatory/inhibitory activity evoke significant interest in neuroscience due to the resulting emergence of strong fluctuations akin to those observed in the resting state of the mammalian brain. While most studies are limited to a δ-like pulse setup, much less is known about the collective behavior in the presence of finite pulse-widths. In this paper, we investigate exponential pulses, with the goal of testing the robustness of previously identified regimes such as the spontaneous emergence of collective irregular dynamics (CID). Moreover, the finite-width assumption paves the way to the investigation of a new ingredient, present in real neuronal networks: the asymmetry between excitatory and inhibitory pulses. Our numerical studies confirm the emergence of CID also in the presence of finite pulse-width, although with a couple of warnings: (i) the amplitude of the collective fluctuations decreases significantly when the pulse-width is comparable to the interspike interval; (ii) CID collapses onto a fully synchronous regime when the inhibitory pulses are sufficient longer than the excitatory ones. Both restrictions are compatible with the recorded behavior of real neurons. Additionally, we find that a seemingly first-order phase transition to a (quasi)-synchronous regime disappears in the presence of a finite width, confirming the peculiarity of the δ-spikes. A tran-sition to synchrony is instead observed upon increasing the ratio between the width of inhibitory and excitatory pulses: this transition is accompanied by a hysteretic region, which shrinks upon increasing the network size. Interestingly, for a connectivity comparable to that of the mammalian brain, such a finite-size effect is still sizable. Our numerical studies might help to understand abnormal synchronisation in neurological disorders.