Geodesic
On uniqueness and stability of a cycle in one gene network
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 464-473

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We describe necessary and suffcient conditions for uniqueness and stability of a cycle in an invariant domain of phase portrait of one Glass-Pasternack type block-linear dynamical system that simulates functioning of one natural gene network. Existence of such a cycle, geometry and combinatorics of phase portraits of similar systems were studied in our previous publications.
Keywords: circular gene network, fixed points, piecewise linear dynamical systems, Poincaré map.
Mots-clés : cycles, phase portraits, invariant domains 
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     author = {V. P. Golubyatnikov and L. S. Minushkina},
     title = {On uniqueness and stability of a cycle in one gene network},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a29/}
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V. P. Golubyatnikov; L. S. Minushkina. On uniqueness and stability of a cycle in one gene network. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 464-473. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a29/