### Abstract

We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

Original language | English (US) |
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Pages (from-to) | 453-462 |

Number of pages | 10 |

Journal | Sheng li xue bao : [Acta physiologica Sinica] |

Volume | 63 |

Issue number | 5 |

State | Published - Oct 25 2011 |

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### ASJC Scopus subject areas

- Physiology

### Cite this

*Sheng li xue bao : [Acta physiologica Sinica]*,

*63*(5), 453-462.

**Statistical physics approaches to neuronal network dynamics.** / Cai, David; Tao, Louis.

Research output: Contribution to journal › Article

*Sheng li xue bao : [Acta physiologica Sinica]*, vol. 63, no. 5, pp. 453-462.

}

TY - JOUR

T1 - Statistical physics approaches to neuronal network dynamics.

AU - Cai, David

AU - Tao, Louis

PY - 2011/10/25

Y1 - 2011/10/25

N2 - We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

AB - We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

UR - http://www.scopus.com/inward/record.url?scp=84874174650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874174650&partnerID=8YFLogxK

M3 - Article

VL - 63

SP - 453

EP - 462

JO - Acta Physiologica Sinica

JF - Acta Physiologica Sinica

SN - 0371-0874

IS - 5

ER -