D3 Dihedral Logistic Map of Fractional Order

Marius-F. Danca; Nikolay Kuznetsov

doi:10.20944/preprints202112.0303.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 17 December 2021 / Approved: 20 December 2021 / Online: 20 December 2021 (10:20:56 CET)

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Discrete fractional-order system; Caputo delta fractional difference; Hidden attractor; Dihedral symmetry D3

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

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D3 Dihedral Logistic Map of Fractional Order

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