| Full text | |
| Author(s): |
Total Authors: 4
|
| Affiliation: | [1] Univ Buenos Aires, Buenos Aires, DF - Argentina
[2] Univ Sao Paulo, Sao Paulo - Brazil
[3] Univ Miami, Coral Gables, FL 33124 - USA
[4] Univ Paris Seine, Cergy - France
Total Affiliations: 4
|
| Document type: | Journal article |
| Source: | Journal of Statistical Physics; v. 172, n. 6, p. 1564-1575, SEP 2018. |
| Web of Science Citations: | 1 |
| 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 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. (AU) | |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |