Abstract:
We consider the system of two coupled one-dimensional parabola maps. It is well known
that the parabola map is the simplest map that can exhibit chaotic dynamics, chaos in this map
appears through an infinite cascade of period-doubling bifurcations. For two coupled parabola
maps we focus on studying attractors of two types: those which resemble the well-known discrete
Lorenz-like attractors and those which are similar to the discrete Shilnikov attractors. We describe
and illustrate the scenarios of occurrence of chaotic attractors of both types.
This paper was supported by the RSF grant 17-11-01041. Numerical results presented in Section 3 were
obtained with the assistance of the Laboratory of Dynamical Systems and Applications NRU HSE, of
the Ministry of Science and Higher Education of the RF grant No. 075-15-2019-1931. E. Karatetskaia
acknowledges the Russian Foundation for Basic Research, grant No. 19-02-00610 for the support of
scientific research.
Citation:
E. Kuryzhov, E. Karatetskaia, D. Mints, “Lorenz- and Shilnikov-Shape Attractors
in the Model of Two Coupled Parabola Maps”, Rus. J. Nonlin. Dyn., 17:2 (2021), 165–174
\Bibitem{KurKarMin21}
\by E. Kuryzhov, E. Karatetskaia, D. Mints
\paper Lorenz- and Shilnikov-Shape Attractors
in the Model of Two Coupled Parabola Maps
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 2
\pages 165--174
\mathnet{http://mi.mathnet.ru/nd748}
\crossref{https://doi.org/10.20537/nd210203}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85109502519}
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This publication is cited in the following 1 articles:
Matvey Kulakov, Galina Neverova, Efim Frisman, “The Ricker Competition Model of Two Species: Dynamic Modes and Phase Multistability”, Mathematics, 10:7 (2022), 1076
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