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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 175, Number 1, Pages 62–83
DOI: https://doi.org/10.4213/tmf8441 (Mi tmf8441) 		 
This article is cited in 25 scientific papers (total in 25 papers)

Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations

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

a Yaroslavl State University, Yaroslavl, Russia
b Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (536 kB) Citations (25)
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DOI: https://doi.org/10.4213/tmf8441
Abstract: We consider special systems of ordinary differential equations, so-called circular unidirectional chains. For this class of systems, we develop a new method for studying the existence and stability problems for periodic solutions. A feature of the proposed approach is that some auxiliary systems with delay are used in both seeking cycles and analyzing their stability properties. We illustrate the relevance of this approach with a concrete example of a circular Hopfield neural network.
Keywords: chain of unidirectionally coupled equations, system with delay, Hopfield neural network, periodic solution, asymptotic behavior, stability.
Received: 14.11.2012
Revised: 23.11.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 175, Issue 1, Pages 499–517
DOI: https://doi.org/10.1007/s11232-013-0041-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations”, TMF, 175:1 (2013), 62–83; Theoret. and Math. Phys., 175:1 (2013), 499–517
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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