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Neural fields with fast learning dynamic kernel

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Abstract

We introduce a modified-firing-rate model based on Hebbian-type changing synaptic connections. The existence and stability of solutions such as rest state, bumps, and traveling waves are shown for this type of model. Three types of kernels, namely exponential, Mexican hat, and periodic synaptic connections, are considered. In the former two cases, the existence of a rest state solution is proved and the conditions for their stability are found. Bump solutions are shown for two kinds of synaptic kernels, and their stability is investigated by constructing a corresponding Evans function that holds for a specific range of values of the kernel coefficient strength (KCS). Applying a similar method, we consider exponential synaptic connections, where traveling wave solutions are shown to exist. Simulation and numerical analysis are presented for all these cases to illustrate the resulting solutions and their stability.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    A. H. Abbassian, M. Fotouhi & M. Heidari

  2. Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran

    M. Fotouhi

  3. Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran

    M. Heidari

Authors
  1. A. H. Abbassian
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  2. M. Fotouhi
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  3. M. Heidari
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Corresponding author

Correspondence to M. Fotouhi.

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Abbassian, A.H., Fotouhi, M. & Heidari, M. Neural fields with fast learning dynamic kernel. Biol Cybern 106, 15–26 (2012). https://doi.org/10.1007/s00422-012-0475-9

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  • DOI: https://doi.org/10.1007/s00422-012-0475-9

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