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On a method for mathematical modeling of chemical synapses

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Abstract

We introduce a new mathematical model of a circular neural network with unidirectional chemical bonds. The model is a singularly perturbed system of delay differential-difference equations. We study the existence and stability of relaxation periodic motions in the system. It is proved that the well-known buffer phenomenon can occur in the model.

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References

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Authors and Affiliations

  1. Yaroslavl State University, Yaroslavl, Russia

    S. D. Glyzin, A. Yu. Kolesov & N. Kh. Rozov

  2. Moscow State University, Moscow, Russia

    S. D. Glyzin, A. Yu. Kolesov & N. Kh. Rozov

Authors
  1. S. D. Glyzin
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  2. A. Yu. Kolesov
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  3. N. Kh. Rozov
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Additional information

Original Russian Text © S.D. Glyzin, A.Yu. Kolesov, N.Kh. Rozov, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 10, pp. 1227–1244.

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Glyzin, S.D., Kolesov, A.Y. & Rozov, N.K. On a method for mathematical modeling of chemical synapses. Diff Equat 49, 1193–1210 (2013). https://doi.org/10.1134/S0012266113100017

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  • DOI: https://doi.org/10.1134/S0012266113100017

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