Geodesic
On invariant surfaces in phase portraits
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 5-13

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For block-linear dynamical system of dimensions 3 and 4 considered as models of simplest circular gene networks, we find sufficient conditions of existence of invariant surfaces in their phase portraits. These surfaces contain periodic trajectories of the dynamical systems.
Keywords: block-linear dynamical systems, Poincaré map, fixed point, Grobman—Hartman theorem, Perron—Frobenius theorem. .
Mots-clés : invariant domains, invariant surfaces, cycles 
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     title = {On invariant surfaces in phase portraits},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a0/}
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N. B. Ayupova; V. P. Golubyatnikov; L. S. Minushkina. On invariant surfaces in phase portraits. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 5-13. http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a0/