### Abstract

Stochastic properties of neurons with shunt type inhibition which have Poisson pulse inputs are considered. The shunt type inhibition lowers the neuron potential in the form of division. In this case the neuron model becomes a system with state dependent noise. The transition probability density function and the first passage time density function of the neuron potential are important. These quantities satisfy Kolmogorov's equation and the law of probability conservation. However, analytical solution cannot be obtained except in very simple cases and hence the numerical method is used together with the analytical one. The results calculated for shunt type inhibition are compared with those for subtractive inhibition.

Original language | English |
---|---|

Title of host publication | Syst Comput Controls |

Pages | 26-33 |

Number of pages | 8 |

Volume | 5 |

Edition | 4 |

Publication status | Published - 1974 Jul |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Syst Comput Controls*(4 ed., Vol. 5, pp. 26-33)

**STOCHASTIC PROPERTIES OF NEURONS WITH SHUNT TYPE INHIBITION.** / Matsuyama, Yasuo; Shirai, Katsuhiko; Akizuki, Kageo.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Syst Comput Controls.*4 edn, vol. 5, pp. 26-33.

}

TY - CHAP

T1 - STOCHASTIC PROPERTIES OF NEURONS WITH SHUNT TYPE INHIBITION.

AU - Matsuyama, Yasuo

AU - Shirai, Katsuhiko

AU - Akizuki, Kageo

PY - 1974/7

Y1 - 1974/7

N2 - Stochastic properties of neurons with shunt type inhibition which have Poisson pulse inputs are considered. The shunt type inhibition lowers the neuron potential in the form of division. In this case the neuron model becomes a system with state dependent noise. The transition probability density function and the first passage time density function of the neuron potential are important. These quantities satisfy Kolmogorov's equation and the law of probability conservation. However, analytical solution cannot be obtained except in very simple cases and hence the numerical method is used together with the analytical one. The results calculated for shunt type inhibition are compared with those for subtractive inhibition.

AB - Stochastic properties of neurons with shunt type inhibition which have Poisson pulse inputs are considered. The shunt type inhibition lowers the neuron potential in the form of division. In this case the neuron model becomes a system with state dependent noise. The transition probability density function and the first passage time density function of the neuron potential are important. These quantities satisfy Kolmogorov's equation and the law of probability conservation. However, analytical solution cannot be obtained except in very simple cases and hence the numerical method is used together with the analytical one. The results calculated for shunt type inhibition are compared with those for subtractive inhibition.

UR - http://www.scopus.com/inward/record.url?scp=0016079143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016079143&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0016079143

VL - 5

SP - 26

EP - 33

BT - Syst Comput Controls

ER -