We investigate the occurrence of quasisynchronous events in a random network of excitatory leaky integrateand-fire neurons equipped with short-term plasticity. The dynamics is analyzed by monitoring both the evolution of global synaptic variables and, on a microscopic ground, the interspike intervals of the individual neurons. We find that quasisynchronous events are the result of a mixture of synchronized and unsynchronized motion, analogously to the emergence of synchronization in the

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... tion in the Kuramoto model. In the present context, disorder is due to the random structure of the network and thereby vanishes for a diverging network size N (i.e., in the thermodynamic limit), when statistical fluctuations become negligible. Remarkably, the fraction of asynchronous neurons remains strictly larger than zero for arbitrarily large N . This is due to the presence of a robust homoclinic cycle in the self-generated synchronous dynamics. The nontrivial large-N behavior is confirmed by the anomalous scaling of the maximum Lyapunov exponent, which is strictly positive in a finite network and decreases as N −0.27 . Finally, we have checked the robustness of this dynamical phase with respect to the addition of noise, applied to either the reset potential or the leaky current.