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On Invariant Surfaces in the Phase Portraits of Models of Circular Gene Networks

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Abstract

For block-linear dynamical systems of dimensions 3 and 4 considered as models of simplest circular gene networks, we find sufficient conditions for the existence of invariant surfaces in their phase portraits. These surfaces contain periodic trajectories of the dynamical systems.

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ACKNOWLEDGMENTS

The authors are sincerely grateful to S.A. Kantor for useful advice and discussions and also to the anonymous referee for critical remarks.

Funding

The work was carried out within the framework of the state order for the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0009.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    N. B. Ayupova, V. P. Golubyatnikov & L. S. Minushkina

Authors
  1. N. B. Ayupova
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  2. V. P. Golubyatnikov
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  3. L. S. Minushkina
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Correspondence to N. B. Ayupova, V. P. Golubyatnikov or L. S. Minushkina.

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Translated by V. Potapchouck

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Ayupova, N.B., Golubyatnikov, V.P. & Minushkina, L.S. On Invariant Surfaces in the Phase Portraits of Models of Circular Gene Networks. J. Appl. Ind. Math. 16, 589–595 (2022). https://doi.org/10.1134/S1990478922040019

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  • DOI: https://doi.org/10.1134/S1990478922040019

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