Geodesic
On stucture of phase portrait of one 5-dimensional gene network model
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 19-29

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We obtain conditions of uniqueness of a cycle in phase portrait of one piecewise linear dynamical system which simulates functioning of a circular gene network with five components regulated by neagtive feedbacks only. We describe behavior of trajectories of this system in its invariant toric domain, and show stability of that cycle.
Keywords: circular gene network model, negative feedbacks, piecewise-linear dynamical systems, Poincaré mapping, monotonicity, fixed point, stability. .
Mots-clés : phase portrait, invariant domains, cycles 
@article{SJIM_2021_24_3_a1,
     author = {N. B. Ayupova and V. P. Golubyatnikov},
     title = {On stucture of phase portrait  of one 5-dimensional gene network model},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {19--29},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a1/}
}
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N. B. Ayupova; V. P. Golubyatnikov. On stucture of phase portrait  of one 5-dimensional gene network model. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 19-29. http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a1/