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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
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.
Received: 19.04.2021 Accepted: 21.05.2021
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
Linking options:
https://www.mathnet.ru/eng/nd748 https://www.mathnet.ru/eng/nd/v17/i2/p165
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