Phase Transition for Infinite Systems of Spiking Neurons

P. A. Ferrari, A. Galves, I. Grigorescu, E. Löcherbach

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 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 γ> 0. For this process we prove the existence of a value γc such that the system has one or two extremal invariant measures according to whether γ> γc or not.

Original languageEnglish (US)
Pages (from-to)1564-1575
Number of pages12
JournalJournal of Statistical Physics
Issue number6
StatePublished - Sep 1 2018


  • Additivity and duality
  • Interacting point processes with memory of variable length
  • Phase transition
  • Systems of spiking neurons

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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