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arXiv · 2204.07825

Symmetry-breaking and bifurcation diagrams of fractional-order maps

Marius-F. Danca
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Abstract

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.

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Marius-F. Danca. 2022-04-16. Symmetry-breaking and bifurcation diagrams of fractional-order maps. https://arxiv.org/abs/2204.07825

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