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Mathematical analysis of a neural network with inhibitory coupling

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  • Cottrell, Marie

Abstract

We study the role of inhibition in a nearest-neighbours-connected neural model. The state of the network is a Markov process of which we study the ergodic properties or divergence characteristics using the parameters of the system. We prove that, when inhibition is smaller than a certain threshold, the network is ergodic and works in a stationary way. Conversely, when inhibition increases, the network is divided into two groups: active and inactive neurons. We observe by means of computer simultation that striped or moiré responses appear, whose shape and width depend on considered neighbourhood size. The model resembles the biological reality of the young animal's cerebellar cortex.

Suggested Citation

  • Cottrell, Marie, 1992. "Mathematical analysis of a neural network with inhibitory coupling," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 103-126, February.
    • Handle: RePEc:eee:spapps:v:40:y:1992:i:1:p:103-126
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    Cited by:

    1. Turova, Tatyana S., 1998. "Exponential rate of convergence of an infinite neuron model with local connections," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 173-193, March.
    2. Marie Cottrell & Tatyana S. Turova, 1999. "Use of an Hourglass Model in Neuronal Coding," Cahiers de la Maison des Sciences Economiques r99024, Université Panthéon-Sorbonne (Paris 1).
    3. Marie Cottrell & Tatyana S Turova, 1999. "Use of an Hourglass Model in Neuronal Coding," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03707112, HAL.
    4. Marie Cottrell & Tatyana S Turova, 1999. "Use of an Hourglass Model in Neuronal Coding," Post-Print halshs-03707112, HAL.

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