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Izvestiya: Mathematics, 2013, Volume 77, Issue 2, Pages 271–312
DOI: https://doi.org/10.1070/IM2013v077n02ABEH002636 (Mi im7960) 		 
This article is cited in 34 scientific papers (total in 34 papers)

Relaxation self-oscillations in Hopfield networks with delay

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
English version PDF (620 kB) Citations (34)
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DOI: https://doi.org/10.1070/IM2013v077n02ABEH002636
Abstract: We consider two singularly perturbed non-linear systems of differential-difference equations with delay; one of them is a mathematical model of a single Hopfield neuron and the other simulates the functioning of a circular network of three or more neurons connected unidirectionally. We study the problems of existence, asymptotic behaviour, and stability for these systems of relaxation periodic motions.
Keywords: differential-difference equations, Hopfield neuron networks, relaxation cycle, stability, buffer property.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00384-а
12-01-00155-a
Received: 06.02.2012
Revised: 20.04.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 2, Pages 53–96
DOI: https://doi.org/10.4213/im7960
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
MSC: Primary 34C05; Secondary 34C25, 34C26
Language: English
Original paper language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Relaxation self-oscillations in Hopfield networks with delay”, Izv. RAN. Ser. Mat., 77:2 (2013), 53–96; Izv. Math., 77:2 (2013), 271–312
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v77/i2/p53
    • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:197
    English version PDF:15
    References:97
    First page:43
     
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