A brief note on fractal dynamics of fractional Mandelbrot sets

Yupin Wang, Xiaodi Li, Da Wang and Shutang Liu

Applied Mathematics and Computation, 2022, vol. 432, issue C

Abstract: This paper preliminary examines a kind of Mandelbrot set generated by a fractional difference 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 visualized to illustrate the main conclusions.

Keywords: Fractal; Quadratic map; Discrete fractional calculus; Connectivity; Disturbance (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:432:y:2022:i:c:s0096300322004271

DOI: 10.1016/j.amc.2022.127353

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