On uniqueness and stability of a cycle in one gene network

V. P. Golubyatnikov ; L. S. Minushkina

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 464-473.

Résumé

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.

Détail

Keywords: circular gene network, fixed points, piecewise linear dynamical systems, Poincaré map.
Mots-clés : cycles, phase portraits, invariant domains

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