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This article is cited in 4 scientific papers (total in 4 papers)
Structure of the phase portrait of a piecewise-linear dynamical system
N. B. Ayupovaab, V. P. Golubyatnikovac a Sobolev Institute of Mathematics SB RAS,
pr. Akad. Koptyuga 4,
630090 Novosibirsk
b Novosibirsk State University,
ul. Pirogova 1,
630090 Novosibirsk
c Yakovlev Novosibirsk Military Institute,
ul. Kluch-Kamyshenskoe Plato 6/2,
630114 Novosibirsk
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.
Keywords:
block-linear dynamical systems, phase portraits,
invariant surfaces, cycles, Poincaré mapping,
gene network models, Hopf link.
Received: 05.07.2019 Revised: 05.07.2019 Accepted: 05.09.2019
Citation:
N. B. Ayupova, V. P. Golubyatnikov, “Structure of the phase portrait of a piecewise-linear dynamical system”, Sib. Zh. Ind. Mat., 22:4 (2019), 19–25; J. Appl. Industr. Math., 13:4 (2019), 606–611
Linking options:
https://www.mathnet.ru/eng/sjim1061 https://www.mathnet.ru/eng/sjim/v22/i4/p19
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Abstract page: | 258 | Full-text PDF : | 156 | References: | 27 | First page: | 3 |
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