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Structure of Phase Portraits of Nonlinear Dynamical Systems

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We consider phase portraits of some piecewise linear dynamical systems of chemical kinetics. We construct an invariant piecewise linear surface that consists of eight planar polygons and is formed by the trajectories which do not enter the attraction basin of a stable cycle. We prove that the dynamical system does not have cycles on this surface. Bibliography: 26 titles. Illustrations: 1 figure.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga Av., Novosibirsk, 630090, Russia

    V. P. Golubyatnikov

  2. Novosibirsk State University, 2, ul. Pirogova, Novosibirsk, 630090, Russia

    V. P. Golubyatnikov & A. E. Kalenykh

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  1. V. P. Golubyatnikov
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  2. A. E. Kalenykh
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Correspondence to V. P. Golubyatnikov.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 15, No. 1, 2015, pp. 45-53.

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Golubyatnikov, V.P., Kalenykh, A.E. Structure of Phase Portraits of Nonlinear Dynamical Systems. J Math Sci 215, 475–483 (2016). https://doi.org/10.1007/s10958-016-2852-8

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  • DOI: https://doi.org/10.1007/s10958-016-2852-8

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