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

    2021, Vol. 17, no. 2, pp.  165-174

    Author(s): Kuryzhov E., Karatetskaia E., Mints D.

    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
    Citation: Kuryzhov E., Karatetskaia E., Mints D., Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp.  165-174
    DOI:10.20537/nd210203


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