Geodesic
On cycles in models of functioning of circular gene networks
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 54-63

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We study a phase portrait of a nonlinear 10-dimensional dynamical system describing a model of functioning of one circular gene network. We find sufficient conditions for the existence of a cycle in this phase portrait. For a similar 18-dimensional dynamical system, we find conditions for the existence of at least two cycles in its phase portrait.
Keywords: nonlinear dynamical systems, circular gene network, torus principle.
Mots-clés : phase portraits, cycles 
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     author = {V. P. Golubyatnikov and N. E. Kirillova},
     title = {On cycles in models of functioning of circular gene networks},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {54--63},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_1_a4/}
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V. P. Golubyatnikov; N. E. Kirillova. On cycles in models of functioning of circular gene networks. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 54-63. http://geodesic.mathdoc.fr/item/VNGU_2018_18_1_a4/