Geodesic
Buffering in cyclic gene networks
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 560-579 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider cyclic chains of unidirectionally coupled delay differential–difference equations that are mathematical models of artificial oscillating gene networks. We establish that the buffering phenomenon is realized in these system for an appropriate choice of the parameters{:} any given finite number of stable periodic motions of a special type, the so-called traveling waves, coexist.
Keywords: cyclic chain of unidirectionally coupled equations, artificial gene network, traveling wave, asymptotic behavior, stability, buffering. 
@article{TMF_2016_187_3_a9,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {Buffering in cyclic gene networks},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {560--579},
     year = {2016},
     volume = {187},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a9/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - A. Yu. Kolesov
AU  - N. Kh. Rozov
TI  - Buffering in cyclic gene networks
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 560
EP  - 579
VL  - 187
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a9/
LA  - ru
ID  - TMF_2016_187_3_a9
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A A. Yu. Kolesov
%A N. Kh. Rozov
%T Buffering in cyclic gene networks
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 560-579
%V 187
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a9/
%G ru
%F TMF_2016_187_3_a9
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Buffering in cyclic gene networks. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 560-579. http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a9/

[1] M. B. Elowitz, S. Leibler, Nature, 403:6767 (2000), 335–338 | DOI

[2] A. N. Tikhonov, Matem. sb., 31(73):3 (1952), 575–586 | MR | Zbl

[3] E. P. Volokitin, Sib. zhurn. industr. matem., 7:3 (2004), 57–65 | MR | Zbl

[4] O. Buse, A. Kuznetsov, R. A. Pérez, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19:12 (2009), 4097–4106 | DOI | MR | Zbl

[5] O. Buse, R. Pérez, A. Kuznetsov, Phys. Rev. E, 81:6 (2010), 066206, 7 pp. | DOI | MR

[6] V. A. Likhoshvai, Yu. G. Matushkin, S. I. Fadeev, Sib. zhurn. industr. matem., 6:2 (2003), 64–80 | MR | Zbl

[7] G. V. Demidenko, N. A. Kolchanov, V. A. Likhoshvai, Yu. G. Matushkin, S. I. Fadeev, Zh. vychisl. matem. i matem. fiz., 44:12 (2004), 2276–2295 | MR | Zbl

[8] S. I. Fadeev, V. A. Likhoshvai, Sib. zhurn. industr. matem., 6:3 (2003), 134–153 | MR | Zbl

[9] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, Izv. RAN. Ser. matem., 77:2 (2013), 53–96 | DOI | MR | Zbl

[10] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, TMF, 175:1 (2013), 62–83 | DOI | MR | Zbl

[11] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, Izv. RAN. Ser. matem., 78:4 (2014), 73–108 | DOI | DOI | MR | Zbl

[12] A. Yu. Kolesov, E. F. Mischenko, N. Kh. Rozov, “Rele s zapazdyvaniem i ego $C^1$-approksimatsiya”, Dinamicheskie sistemy i smezhnye voprosy, Sb. statei. K 60-letiyu so dnya rozhdeniya akademika Dmitriya Viktorovicha Anosova, Tr. MIAN, 216, Nauka, M., 1997, 126–153 | MR | Zbl

[13] A. Yu. Kolesov, E. F. Mischenko, N. Kh. Rozov, Zh. vychisl. matem. i matem. fiz., 50:12 (2010), 2099–2112 | DOI | MR | Zbl

[14] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, Differents. uravn., 47:7 (2011), 919–932 | MR | Zbl

[15] S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, Differents. uravn., 49:10 (2013), 1227–1244 | MR | Zbl