Geodesic
On invariant surfaces in gene network models
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 69-76

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We construct an invariant two-dimensional surface in the phase portrait of a certain six-dimensional dynamical system which is considered as a model for the circular gene network functioning. This invariant surface contains an equilibrium point $S_0$ of the system, and if $S_0$ is hyperbolic then this surface contains a cycle of the system. The conditions for the existence of a cycle of this and similar systems were obtained earlier.
Keywords: circular gene network model, cycle, hyperbolic equilibrium point
Mots-clés : phase portrait, invariant surface. . 
@article{SJIM_2020_23_4_a4,
     author = {N. E. Kirillova},
     title = {On invariant surfaces in gene network models},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {69--76},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a4/}
}
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N. E. Kirillova. On invariant surfaces in gene network models. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 69-76. http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a4/