Geodesic
On a mathematical model of the repressilator
Algebra i analiz, Tome 33 (2021) no. 5, pp. 80-124.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2021_33_5_a2,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {On a mathematical model of the repressilator},
     journal = {Algebra i analiz},
     pages = {80--124},
     publisher = {mathdoc},
     volume = {33},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2021_33_5_a2/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - A. Yu. Kolesov
AU  - N. Kh. Rozov
TI  - On a mathematical model of the repressilator
JO  - Algebra i analiz
PY  - 2021
SP  - 80
EP  - 124
VL  - 33
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2021_33_5_a2/
LA  - ru
ID  - AA_2021_33_5_a2
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A A. Yu. Kolesov
%A N. Kh. Rozov
%T On a mathematical model of the repressilator
%J Algebra i analiz
%D 2021
%P 80-124
%V 33
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2021_33_5_a2/
%G ru
%F AA_2021_33_5_a2
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. On a mathematical model of the repressilator. Algebra i analiz, Tome 33 (2021) no. 5, pp. 80-124. http://geodesic.mathdoc.fr/item/AA_2021_33_5_a2/

[1] Elowitz M. B., Leibler S., “A synthetic oscillatory network of transcriptional regulators”, Nature, 403 (2000), 335–338 | DOI

[2] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry pri proizvodnykh”, Mat. sb., 31:3 (1952), 575–586 | Zbl

[3] Volokitin E. P., “O predelnykh tsiklakh v prosteishei modeli gipoteticheskoi gennoi seti”, Sib. zh. industr. mat., 7:3 (2004), 57–65 | MR | Zbl

[4] Buse O., Kuznetsov A., Pérez R. A., “Existence of limit cycles in the repressilator equations”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19:12 (2009), 4097–4106 | DOI | MR | Zbl

[5] Buse O., Pérez A., Kuznetsov A., “Dynamical properties of the repressilator model”, Phys. Rev. E (3), 81:6 (2010), 066206 | DOI | MR

[6] Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Zadachi teorii funktsionirovaniya gennykh setei”, Sib. zh. industr. mat., 6:2 (2003), 64–80 | MR | Zbl

[7] Demidenko G. V., Kolchanov N. A., Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Matematicheskoe modelirovanie regulyarnykh konturov gennykh setei”, Zh. vychisl. mat. mat. fiz., 44:12 (2004), 2276–2295 | MR | Zbl

[8] Fadeev S. I., Likhoshvai V. A., “O gipoteticheskikh gennykh setyakh”, Sib. zh. industr. mat., 6:3 (2003), 134–153 | MR | Zbl

[9] Kolesov A. Yu., Rozov N. Kh., Sadovnichii V. A., “Periodicheskie resheniya tipa beguschikh voln v koltsevykh gennykh setyakh”, Izv. RAN. Ser. mat., 80:3 (2016), 67–94 | MR | Zbl

[10] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Suschestvovanie i ustoichivost relaksatsionnogo tsikla v matematicheskoi modeli repressilyatora”, Mat. zametki, 101:1 (2017), 58–76 | MR | Zbl

[11] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Ob odnom podkhode k matematicheskomu modelirovaniyu iskusstvennykh gennykh setei”, Teor. mat. fiz., 194:3 (2018), 547–568 | MR | Zbl

[12] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Kvaziustoichivye struktury v koltsevykh gennykh setyakh”, Zh. vychisl. mat. i mat. fiz., 58:5 (2018), 682–704

[13] Kolesov A. Yu., Kolesov Yu. S., “Relaksatsionnye kolebaniya v matematicheskikh modelyakh ekologii”, Tr. Mat. in-ta RAN, 199, 1993, 3–124

[14] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Relaksatsionnye avtokolebaniya v setyakh Khopfilda s zapazdyvaniem”, Izv. RAN. Ser. mat., 77:2 (2013), 53–96 | MR | Zbl

[15] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Periodicheskie resheniya tipa beguschikh voln v koltsevykh tsepochkakh odnonapravlenno svyazannykh uravnenii”, Teor. i mat. fiz., 175:1 (2013), 62–83 | Zbl

[16] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v koltsevykh tsepochkakh odnonapravlenno svyazannykh generatorov”, Izv. RAN. Ser. mat., 78:4 (2014), 73–108 | MR | Zbl