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D3 Dihedral Logistic Map of Fractional Order

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Mathematics, Chaotic Systems: From Mathematics to Real-World Applications, 10(213) (2022) .

Full text: http://dx.doi.org/doi.org/10.3390/math10020213

Author-provided full text:
Post-print (final draft after peer review) - added by Marius Florin Danca

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Abstract

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map
presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of
the bifurcation diagram versus the fractional order requires special attention. The system stability is
determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical
results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in
the fractional-order variant

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