Fractional quantum Julia set

•The q-difference operator is introduced into the study of fractal objects generated from the quadratic map.•Enrich the research of the fractional q-difference system to open up a new viewpoint for exploring their complex dynamics.•Provide potential inspiration for the qualitative analysis and fract...

Full description

Saved in:
Bibliographic Details
Published inApplied mathematics and computation Vol. 453; p. 128077
Main Author Wang, Yupin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2023
Subjects
[formula omitted]-Difference
Disturbance
Fractal
Fractional calculus
Quadratic map
39A33
Fractal
39A13
Disturbance
26A33
28A80
q-Difference
Fractional calculus
Quadratic map
Online AccessGet full text

Cover

More Information
Summary:•The q-difference operator is introduced into the study of fractal objects generated from the quadratic map.•Enrich the research of the fractional q-difference system to open up a new viewpoint for exploring their complex dynamics.•Provide potential inspiration for the qualitative analysis and fractal control of the fractional quantum Julia set. This paper proposes fractional quantum Julia sets based on a fractional q-difference map and preliminarily investigates their fractal dynamic characteristics by numerical methods and graphical explorations. The influence of parameters on the novel fractal sets is performed by dimension analysis. Memory and scale mainly affect the appearance and existence of the sets, respectively. The robustness of the sets to three types of dynamic noise perturbations is discussed by the Julia deviation tools. In particular, the deviation index is fitted concerning noise intensity. Several extensive numerical experiments are done to support the main conclusions.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2023.128077