Phase transition for infinite systems of spiking neurons

Abstract

We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate $1$ whenever its membrane potential is larger than a threshold value. This membrane potential evolves in time and integrates the spikes of all {\it presynaptic neurons} since the last spiking time of the neuron. When a neuron spikes, its membrane potential is reset to $0$ and simultaneously, a constant value is added to the membrane potentials of its postsynaptic neurons. Moreover, each neuron is exposed to a leakage effect leading to an abrupt loss of potential occurring at random times driven by an independent Poisson point process of rate $\gamma >0.$ For this process we prove the existence of a value ${\gamma }_c$ such that the system has one or two extremal invariant measures according to whether $\gamma >{\gamma }_c$ or not.

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• Hydrodynamic limit for interacting neurons
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• A stochastic system with infinite interacting components to model the time evolution of the membrane potentials of a population of neurons

Cited by in corpus (5)

• A Result of Metastability for an Infinite System of Spiking Neurons
• The Effect of Graph Connecitivity on Metastability on a Stochastic System of Spiking Neurons
• Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality
• Metastability in a Stochastic System of Spiking Neurons with Leakage
• Multiple Phase Transitions for an Infinite System of Spiking Neurons