Synchronization of Julia Sets in Three-Dimensional Discrete Financial Models

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-12-09 DOI:10.3390/fractalfract7120872

Zhongyuan Zhao, Yongping Zhang, Dadong Tian

引用次数: 0

Abstract

When aiming to achieve consistency in fractal characteristics between different models, it is crucial to consider the synchronization of Julia sets. This paper studies the synchronization of Julia sets in three-dimensional discrete financial models. First, three-dimensional discrete financial models with different model parameters are proposed and their Julia sets are presented. According to the model forms, two kinds of synchronous couplers that can achieve synchronization of Julia sets between different models are designed by changing the synchronization parameters. The proposed synchronization method is theoretically derived and the efficiency of different synchronous couplers are compared. Finally, the effectiveness is verified by Julia sets graphics. This method has reference value for theoretical research into financial models in the field of fractals.

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三维离散金融模型中朱莉娅集的同步性

为了实现不同模型分形特征的一致性，考虑 Julia 集的同步性至关重要。本文研究了三维离散金融模型中 Julia 集的同步性。首先，提出了具有不同模型参数的三维离散金融模型，并给出了它们的 Julia 集。根据模型形式，通过改变同步参数，设计了两种可实现不同模型间 Julia 集同步的同步耦合器。从理论上推导了所提出的同步方法，并比较了不同同步耦合器的效率。最后，通过 Julia 集图形验证了其有效性。该方法对分形领域的金融模型理论研究具有参考价值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.