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Russian Journal of Nonlinear Dynamics, 2021, Volume 17, Number 2, Pages 165–174
DOI: https://doi.org/10.20537/nd210203
(Mi nd748)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical problems of nonlinearity

Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps

E. Kuryzhov, E. Karatetskaia, D. Mints

National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia
References:
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.
Keywords: strange attractor, discrete Lorenz attractor, hyperchaos, discrete Shilnikov attractor, two-dimensional endomorphism.
Funding agency Grant number
Russian Science Foundation 17-11-01041
Ministry of Education and Science of the Russian Federation 075-15-2019-1931
Russian Foundation for Basic Research 19-02-00610
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.
Received: 19.04.2021
Accepted: 21.05.2021
Bibliographic databases:
Document Type: Article
MSC: 37G35, 37G10
Language: english
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
Citation in format AMSBIB
\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:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian Journal of Nonlinear Dynamics
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