Emergence of a coherent bursting state with scale-free avalanches from collective dynamics of neuronal networks

Human cortex displays spontaneous activity even in the absence of external stimuli. One especially interesting activity gives rise to avalanches or bursts whose size distribution is characterized by a power law. These scale-free neuronal avalanches have been associated with criticality, leading to a hypothesis that the brain operates close to the critical point of a transition between two distinct dynamical states. Despite extensive studies, the mechanism generating scale-free neuronal avalanches and the relation between scale-free avalanches and criticality is not fully understood. We have carried out a computational study of spontaneous activity using networks of neurons connected by conductance-based synapses with uniform excitatory and inhibitory synaptic strength g_E and g_I, and subject to stochastic current. We observe three distinct dynamical states in the parameter space of g_E and g_I: (I) incoherent spiking (II) coherent bursting and (III) incoherent bursting. A high level of synchrony is detected in state II but not in states I and III. Bursting exists in states II and III but not in state I. Scale-free avalanches are found in state II but not in states I and III. At a fixed g_I, the dynamics changes from state I to state II then state III as g_E is increased. Our results thus show that scale-free avalanches occur in the dynamical state of coherent bursting and not at a critical region between two states. Moreover, neither synaptic plasticity nor heavy-tailed synaptic weight distribution are needed.