D3 Dihedral Logistic Map of Fractional Order

Mathematics

Nikolay Kuznetsov¹  Marius-F. Danca² 

[1] Mathematics and Mechanics Faculty, Saint-Petersburg State University, 199034 Saint Petersburg, Russia;STAR-UBB Institute, Babes-Bolyai University, 400084 Cluj-Napoca, Romania;

关键词: discrete fractional-order system;    caputo delta fractional difference;    hidden attractor;    dihedral symmetry D₃;   

DOI  :  10.3390/math10020213

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown