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Izvestiya: Mathematics, 2016, Volume 80, Issue 3, Pages 523–548
DOI: https://doi.org/10.1070/IM8398 (Mi im8398) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Periodic solutions of travelling-wave type in circular gene networks

A. Yu. Kolesova, N. Kh. Rozovb, V. A. Sadovnichiib

a P. G. Demidov Yaroslavl State University
b Lomonosov Moscow State University
English version PDF (452 kB) Citations (21) Russian version article
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DOI: https://doi.org/10.1070/IM8398
Abstract: We consider circular chains of unidirectionally coupled ordinary differential equations which are mathematical models of artificial gene networks. We study the problems of the existence and stability of special periodic solutions, the so-called travelling waves, in these chains. We establish that the number of such periodic solutions grows unboundedly as the number of links in the chain grows. However, at most one of these travelling waves can be stable. We give an explicit algorithm for choosing the stable cycle.
Keywords: chain of unidirectionally coupled equations, artificial gene network, travelling wave, asymptotics, stability.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-04066а
This paper was written with the support of project 1875 of State Request on SRW no. 2014/258 and RFRB (grant no. 15-01-04066a).
Received: 23.04.2015
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 34C25, 92B20, 47N20, 34C05
Language: English
Original paper language: Russian
Citation: A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Periodic solutions of travelling-wave type in circular gene networks”, Izv. Math., 80:3 (2016), 523–548
Citation in format AMSBIB
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\by A.~Yu.~Kolesov, N.~Kh.~Rozov, V.~A.~Sadovnichii
\paper Periodic solutions of travelling-wave type in circular gene networks
\jour Izv. Math.
\yr 2016
\vol 80
\issue 3
\pages 523--548
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    • This publication is cited in the following 21 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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    Abstract page:745
    Russian version PDF:173
    English version PDF:31
    References:67
    First page:50
     
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