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

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Moscow, Russia

    N. B. Ayupova & V. P. Golubyatnikov

  2. Novosibirsk State University, Novosibirsk, Russia

    N. B. Ayupova & V. P. Golubyatnikov

Authors
  1. N. B. Ayupova
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  2. V. P. Golubyatnikov
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Correspondence to N. B. Ayupova.

Additional information

The authors were supported by the Russian Foundation for Basic Research (Grant 12–01–0074) and Interdisciplinary Grant 80 of the Siberian Division of the Russian Academy of Sciences.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 2, pp. 282–289, March–April, 2015.

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Ayupova, N.B., Golubyatnikov, V.P. On two classes of nonlinear dynamical systems: The four-dimensional case. Sib Math J 56, 231–236 (2015). https://doi.org/10.1134/S0037446615020044

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  • DOI: https://doi.org/10.1134/S0037446615020044

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