Abstract
The mathematical model considered here of a neuron system is a chain of an arbitrary number m ≥ 2 of diffusion-coupled singularly perturbed nonlinear delay differential equations with Neumann-type conditions at the endpoints. We study the existence, asymptotic behavior, and stability of relaxation periodic solutions of this system.
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Kashchenko, S.A. and Maiorov, V.V., Modeli volnovoi pamyati (Wave Memory Models), Moscow, 2009.
Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Relaxation Self-Oscillations in Neuron Systems. II, Differ. Uravn., 2011, vol. 47, no. 12, pp. 1675–1692.
Glyzin, S.D., Kolesov, A.Yu., and Rozov, N.Kh., Relaxation Self-Oscillations in Neuron Systems. I, Differ. Uravn., 2011, vol. 47, no. 7, pp. 919–932.
Kolesov, A.Yu. and Rozov, N.Kh., Invariantnye tory nelineinykh volnovykh uravnenii (Invariant Tori of Nonlinear Wave Equations), Moscow, 2004.
Mishchenko, E.F., Sadovnichii, V.A., Kolesov, A.Yu., and Rozov, N.Kh., Avtovolnovye protsessy v nelineinykh sredakh s diffuziei (Autowave Processes in Nonlinear Media with Diffusion), Moscow, 2004.
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Original Russian Text © S.D. Glyzin, A.Yu. Kolesov, N.Kh. Rozov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 2, pp. 155–170.
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Glyzin, S.D., Kolesov, A.Y. & Rozov, N.K. Relaxation self-oscillations in neuron systems: III. Diff Equat 48, 159–175 (2012). https://doi.org/10.1134/S0012266112020012
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DOI: https://doi.org/10.1134/S0012266112020012