2022/04/16 by Marius‐F. Danca, Danca, Marius-F.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2204.07825
openalex publication_date 2022/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper two important aspects related to Caputo fractional-order discrete variant of a class of maps defined on the complex plane, are analytically and numerically revealed: attractors symmetry-broken induced by the fractional-order and the sensible problem of determining the right bifurcation diagram of discrete systems of fractional-order. It is proved that maps of integer order with dihedral symmetry or cycle symmetry loose their symmetry once they are transformed in fractional-order maps. Also, it is conjectured that, contrarily to integer-order maps, determining the bifurcation diagrams of fractional-order maps is far from being a clarified problem. Two examples are considered: dihedral logistic map and cyclic logistic map.