  A collective chaotic phase with power law scaling of activity events is
observed in a disordered mean field network of purely excitatory leaky
integrate-and-fire neurons with short-term synaptic plasticity. The dynamical
phase diagram exhibits two transitions from quasi-synchronous and asynchronous
regimes to the nontrivial, collective, bursty regime with avalanches. In the
homogeneous case without disorder, the system synchronizes and the bursty
behavior is reflected into a doubling-period transition to chaos for a two
dimensional discrete map. Numerical simulations show that the bursty chaotic
phase with avalanches exhibits a spontaneous emergence of time correlations and
enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the
generation of irregular avalanches that emerges from the combination of
disorder and deterministic underlying chaotic dynamics.
