Geodesic
Cycles in the odd-dimensional models of circular gene networks
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 28-38.

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

The necessary and sufficient conditions are obtained for the existence of a cycle in an odd-dimensional nonlinear dynamical system that simulates the functioning of the simplest circular gene network. An invariant neighborhood of this cycle is described which is homeomorphic to a torus.
Keywords: block-linear autonomous system, circular gene network, fixed point of a monotonic mapping, cycle.
Mots-clés : phase portrait 
@article{SJIM_2018_21_4_a2,
     author = {V. P. Golubyatnikov and V. V. Ivanov},
     title = {Cycles in the odd-dimensional models of circular gene networks},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {28--38},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a2/}
}
TY  - JOUR
AU  - V. P. Golubyatnikov
AU  - V. V. Ivanov
TI  - Cycles in the odd-dimensional models of circular gene networks
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2018
SP  - 28
EP  - 38
VL  - 21
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a2/
LA  - ru
ID  - SJIM_2018_21_4_a2
ER  - 
%0 Journal Article
%A V. P. Golubyatnikov
%A V. V. Ivanov
%T Cycles in the odd-dimensional models of circular gene networks
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2018
%P 28-38
%V 21
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a2/
%G ru
%F SJIM_2018_21_4_a2
V. P. Golubyatnikov; V. V. Ivanov. Cycles in the odd-dimensional models of circular gene networks. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 28-38. http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a2/

[1] Akinshin A. A., Golubyatnikov V. P., Golubyatnikov I. V., “O nekotorykh mnogomernykh modelyakh funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matematiki, 16:1 (2013), 3–9 | MR | Zbl

[2] Ayupova N. B., Golubyatnikov V. P., “O edinstvennosti tsikla v trekhmernoi modeli molekulyarnogo repressilyatora”, Sib. zhurn. industr. matematiki, 17:1 (2014), 3–7 | MR | Zbl

[3] Golubyatnikov V. P., Golubyatnikov I. V., “Geometriya i topologiya fazovykh portretov dinamicheskikh sistem Glassa–Pasternaka malykh razmernostei”, Mat. struktury i modelirovanie, 31:3 (2014), 40–47 | Zbl

[4] Golubyatnikov V. P., Golubyatnikov I. V., “O mnogomernykh modelyakh funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matematiki, 13:3 (2010), 13–18 | MR | Zbl

[5] Golubyatnikov V. P., Golubyatnikov I. V., Likhoshvai V. A., “O suschestvovanii i ustoichivosti tsiklov v pyatimernykh modelyakh gennykh setei”, Sib. zhurn. vychisl. matematiki, 13:4 (2010), 403–411 | Zbl

[6] Kazantsev M. V., “O nekotorykh svoistvakh grafov domenov dinamicheskikh sistem”, Sib. zhurn. industr. matematiki, 18:4 (2015), 42–49 | DOI | MR

[7] 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 | DOI | MR | Zbl

[8] Glass L., Pasternack J. S., “Stable oscillations in mathematical models of biological control systems”, J. Math. Biol., 6 (1978), 207–223 | DOI | MR | Zbl

[9] Likhoshvai V. A., Golubyatnikov V. P., Demidenko G. V., Evdokimov A. A., Fadeev S.I., “Teoriya gennykh setei”, Sistemnaya kompyuternaya biologiya, Izd-vo SO RAN, Novosibirsk, 2008, 395–480

[10] Riznichenko G. Yu., Lektsii po matematicheskim modelyam v biologii, M.–Izhevsk, 2011

[11] Golubyatnikov V. P., Ivanov V. V., Minushkina L. S., “O suschestvovanii tsikla v odnoi nesimmetrichnoi modeli koltsevoi gennoi seti”, Sib. zhurn. chistoi i prikl. matematiki, 18:3 (2018), 26–32

[12] Tarski A., “A lattice theoretical fixed point theorem and its applications”, Pacific J. Math., 5 (1955), 285–309 | DOI | MR | Zbl