dorsal/arxiv
View SchemaStochastic dynamics of a finite-size spiking neural network
| Authors | H. Soula, C. C. Chow |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0701042 |
| URL | https://arxiv.org/abs/q-bio/0701042 |
Abstract
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution, mean rate, variance and autocorrelation function of the network activity. The model is applicable to any network where the probability of firing of a neuron in the network only depends on the number of neurons that fired in a previous temporal epoch. Networks with statistically homogeneous connectivity and membrane and synaptic time constants that are not excessively long could satisfy these conditions. Our model completely accounts for the size of the network and correlations in the firing activity. It also allows us to examine how the network dynamics can deviate from mean-field theory. We show that the model and solutions are applicable to spiking neural networks in biophysically plausible parameter regimes.
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"date_modified": "2026-03-02T18:01:35.569000Z",
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"abstract": "We present a simple Markov model of spiking neural dynamics that can be\nanalytically solved to characterize the stochastic dynamics of a finite-size\nspiking neural network. We give closed-form estimates for the equilibrium\ndistribution, mean rate, variance and autocorrelation function of the network\nactivity. The model is applicable to any network where the probability of\nfiring of a neuron in the network only depends on the number of neurons that\nfired in a previous temporal epoch. Networks with statistically homogeneous\nconnectivity and membrane and synaptic time constants that are not excessively\nlong could satisfy these conditions. Our model completely accounts for the size\nof the network and correlations in the firing activity. It also allows us to\nexamine how the network dynamics can deviate from mean-field theory. We show\nthat the model and solutions are applicable to spiking neural networks in\nbiophysically plausible parameter regimes.",
"arxiv_id": "q-bio/0701042",
"authors": [
"H. Soula",
"C. C. Chow"
],
"categories": [
"q-bio.NC"
],
"title": "Stochastic dynamics of a finite-size spiking neural network",
"url": "https://arxiv.org/abs/q-bio/0701042"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "fa68b3c4-66c3-4350-b5c5-84069111303b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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