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Sibirsk. Mat. Zh., 2015, Volume 56, Number 2, Pages 282–289 (Mi smj2638)  

This article is cited in 3 scientific papers (total in 3 papers)

On two classes of nonlinear dynamical systems: The four-dimensional case

N. B. Ayupovaab, V. P. Golubyatnikovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We consider two four-dimensional piecewise linear dynamical systems of chemical kinetics. For one of them, we give an explicit construction of a hypersurface that separates the attraction basins of two stable equilibrium points and contains an unstable cycle of this system. For the other system, we prove the existence of a trajectory not contained in the attraction basin of the stable cycle of this system described earlier by Glass and Pasternack. The homotopy types of the phase portraits of these two systems are compared.

Keywords: nonlinear dynamical system, cycle, invariant manifold, retract.

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English version:
Siberian Mathematical Journal, 2015, 56:2, 231–236

Bibliographic databases:

UDC: 514.745.82
Received: 19.06.2014

Citation: N. B. Ayupova, V. P. Golubyatnikov, “On two classes of nonlinear dynamical systems: The four-dimensional case”, Sibirsk. Mat. Zh., 56:2 (2015), 282–289; Siberian Math. J., 56:2 (2015), 231–236

Citation in format AMSBIB
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\pages 282--289
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\vol 56
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\pages 231--236
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483  mathnet  crossref
    2. V. P. Golubyatnikov, M. V. Kazantsev, “On one piecewise linear dynamical system which models a gene network with variable feedback”, J. Math. Sci., 230:1 (2018), 46–54  mathnet  crossref  crossref
    3. N. B. Ayupova, V. P. Golubyatnikov, M. V. Kazantsev, “On existence of a cycle in one asymmetric model of a molecular repressilator”, Num. Anal. Appl., 10:2 (2017), 101–107  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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