A brief note on fractal dynamics of fractional Mandelbrot sets

被引：15
作者：
Wang, Yupin [1 ]
Li, Xiaodi [1 ]
Wang, Da [2 ]
Liu, Shutang [3 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Shandong, Peoples R China
[2] Shandong Normal Univ, Res Ctr Dynam Syst & Control Sci, Business Sch, Jinan 250358, Shandong, Peoples R China
[3] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 432卷
基金：
中国国家自然科学基金;
关键词：
Fractal; Quadraticmap; Discretefractionalcalculus; Connectivity; Disturbance; GENERALIZED M-SET; DIMENSION; NOISE; ORDER; AREA;
D O I：
10.1016/j.amc.2022.127353
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper preliminary examines a kind of Mandelbrot set generated by a fractional differ-ence quadratic map involving Caputo-like fractional h-difference operators. A connectivity index is proposed based on numerical methods, which avoids difficulties in discussion at the topological level. The dynamics of those sets in two kinds of noise environments are considered involving connectivity, symmetry and dimension. Several typical cases are vi-sualized to illustrate the main conclusions.(c) 2022 Elsevier Inc. All rights reserved.
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页数：8
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