| Full text | |
| Author(s): |
Total Authors: 4
|
| Affiliation: | [1] Univ Aquila, I-67100 Laquila - Italy
[2] Univ Sao Paulo, Sao Paulo - Brazil
[3] Univ Cergy Pontoise, Cergy Pontoise - France
[4] GSSI, Laquila - Italy
Total Affiliations: 4
|
| Document type: | Journal article |
| Source: | Journal of Statistical Physics; v. 158, n. 4, p. 866-902, FEB 2015. |
| Web of Science Citations: | 27 |
| Abstract | |
This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electrical synapses. This system can be informally described as follows. Each neuron spikes randomly following a point process with rate depending on its membrane potential. At its spiking time, the membrane potential of the spiking neuron is reset to the value 0 and, simultaneously, the membrane potentials of the other neurons are increased by an amount of potential 1/N. This mimics the effect of chemical synapses. Additionally, the effect of electrical synapses is represented by a deterministic drift of all the membrane potentials towards the average value of the system. We show that, as the system size N diverges, the distribution of membrane potentials becomes deterministic and is described by a limit density which obeys a non linear PDE which is a conservation law of hyperbolic type. (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 |