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This article is cited in 2 scientific papers (total in 3 papers)
Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev
Numerical Study of Discrete Lorenz-Like Attractors
Alexey Kazakova, Ainoa Murillob, Arturo Vieirocb, Kirill Zaichikova a National Research University Higher School of Economics,
ul. Bolshaya Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia
b Departament de Matemàtiques i Informàtica, Universitat de Barcelona,
Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain
c Centre de Recerca Matematica (CRM),
08193 Bellaterra, Spain
Abstract:
We consider a homotopic to the identity family of maps, obtained as a discretization
of the Lorenz system, such that the dynamics of the last is recovered as a limit dynamics when
the discretization parameter tends to zero. We investigate the structure of the discrete Lorenz-
like attractors that the map shows for different values of parameters. In particular, we check the
pseudohyperbolicity of the observed discrete attractors and show how to use interpolating vector
fields to compute kneading diagrams for near-identity maps. For larger discretization parameter
values, the map exhibits what appears to be genuinely-discrete Lorenz-like attractors, that is,
discrete chaotic pseudohyperbolic attractors with a negative second Lyapunov exponent. The
numerical methods used are general enough to be adapted for arbitrary near-identity discrete
systems with similar phase space structure.
Keywords:
Lorenz attractor, pseudohyperbolicity, interpolating vector fields, kneading dia-
grams
Received: 06.10.2023 Accepted: 01.12.2023
Citation:
Alexey Kazakov, Ainoa Murillo, Arturo Vieiro, Kirill Zaichikov
Linking options:
https://www.mathnet.ru/eng/rcd1246
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Abstract page: | 19 | References: | 7 |
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