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On a modification of the FitzHugh-Nagumo neuron model

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Abstract

A singularly perturbed system of ordinary differential equations with a fast and a slow variable is proposed, which is a modification of the well-known FitzHugh-Nagumo model from neuroscience. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function.

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Authors and Affiliations

  1. Faculty of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia

    S. D. Glyzin & A. Yu. Kolesov

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    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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Correspondence to S. D. Glyzin.

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Original Russian Text © S.D. Glyzin, A.Yu. Kolesov, N.Kh. Rozov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 3, pp. 430–449.

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Glyzin, S.D., Kolesov, A.Y. & Rozov, N.K. On a modification of the FitzHugh-Nagumo neuron model. Comput. Math. and Math. Phys. 54, 443–461 (2014). https://doi.org/10.1134/S0965542514030063

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  • DOI: https://doi.org/10.1134/S0965542514030063

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