Geodesic
Lorenz- and Shilnikov-Shape Attractors
Russian journal of nonlinear dynamics, Tome 17 (2021) no. 2, pp. 165-174

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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. 
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     author = {E. Kuryzhov and E. Karatetskaia and D. Mints},
     title = {Lorenz- and {Shilnikov-Shape} {Attractors}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {165--174},
     publisher = {mathdoc},
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     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2021_17_2_a2/}
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E. Kuryzhov; E. Karatetskaia; D. Mints. Lorenz- and Shilnikov-Shape Attractors. Russian journal of nonlinear dynamics, Tome 17 (2021) no. 2, pp. 165-174. http://geodesic.mathdoc.fr/item/ND_2021_17_2_a2/