# Phase Transition for Infinite Systems of Spiking Neurons

@article{Ferrari2018PhaseTF, title={Phase Transition for Infinite Systems of Spiking Neurons}, author={Pablo Augusto Ferrari and Antonio Galves and Ilie Grigorescu and Eva L{\"o}cherbach}, journal={Journal of Statistical Physics}, year={2018}, volume={172}, pages={1564-1575} }

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 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… CONTINUE READING

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