Abstract
We consider some piecewise linear 4-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass-Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.
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Acknowledgment
The authors express their sincere gratitude to V. G. Bardakov, M. V. Neschadim, and V. A. Churkin for useful discussions and critical remarks.
Funding
The authors were supported by the Russian Foundation for Basic Research (project no. 18-01-00057) and Program No. I.5.1 of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2018-0011).
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Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2019, Vol. XXII, No. 4, pp. 19-25.
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Ayupova, N.B., Golubyatnikov, V.P. Structure of the Phase Portrait of a Piecewise-Linear Dynamical System. J. Appl. Ind. Math. 13, 606–611 (2019). https://doi.org/10.1134/S1990478919040033
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DOI: https://doi.org/10.1134/S1990478919040033