Abstract
We construct an invariant two-dimensional surface in the phase portrait of a certain six-dimensional dynamical system 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.
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ACKNOWLEDGMENTS
The author is grateful to N. B. Ayupova and V. P. Golubyatnikov for necessary recommendations and discussions, the anonymous reviewer for the helpful remarks, and V. N. Dyatlov for technical assistance.
Funding
The author was supported by the Russian Foundation for Basic Research (project no. 20–31–90011) and the Mathematical Center in Akademgorodok (Agreement no. 075-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation).
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Translated by L.B. Vertgeim
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Kirillova, N.E. On Invariant Surfaces in Gene Network Models. J. Appl. Ind. Math. 14, 666–671 (2020). https://doi.org/10.1134/S1990478920040055
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DOI: https://doi.org/10.1134/S1990478920040055