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We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-LIF neurons in the presence of short-term synaptic plasticity. By varying the coupling strength among neurons, we show that a complex chaotic dynamics arises, characterized by scale free avalanches. The origin of this phenomenon in the c-LIF can be related to the order symmetry breaking in neurons spike-times, which corresponds to the onset of a broad activity distribution. Our analysis uncovers a general mechanism through which networks of simple neurons can be attracted to a complex basin in the phase space.
Curies principle states that when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them. We demonstrate that symmetry equivariant neural networks uphold Curies principle and can be used to articulate many s
Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the bre
In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reacti
We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase-lock with a
Experimental and numerical results suggest that the brain can be viewed as a system acting close to a critical point, as confirmed by scale-free distributions of relevant quantities in a variety of different systems and models. Less attention has rec