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FORMATTING OF JULIA SETS OF COMPLEX DYNAMIC SYSTEMS

MIAO OUYANG

School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, P. R. China

E-mail Address: mouyang@mail.sdu.edu.cn

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and

SHUTANG LIU

https://orcid.org/0000-0003-2281-9378

School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, P. R. China

E-mail Address: stliu@sdu.edu.cn

E-mail Address: stliu618@163.com

Corresponding author.

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https://doi.org/10.1142/S0218348X21500699Cited by:1 (Source: Crossref)

Abstract

It is of crucial significance to study a class of complex dynamic planar and spatial systems with disparate coefficients by taking advantage of thoughts of Julia set. In this paper, we present theoretical control methods for the stable domain and Julia sets of systems. Then, we utilize symmetry to exhibit the forms of compositional Julia sets of complex dynamic planar systems. Furthermore, by selecting different coefficients, the location, size, area and shape of Julia set can be controlled, the spatial Julia sets also have certain characteristics, this supplies a possible reference for how to control the stable domain of specific complex dynamic systems. The simulation results are in good agreement with the effectiveness of the methods.

Keywords:

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