Fractal dimension and synchronization of the controlled Julia sets of the SIRS model-Reference-Cited by-同舟云学术

Fractal dimension and synchronization of the controlled Julia sets of the SIRS model

Published:2019-10 Issue:07 Volume:12 Page:1950085
ISSN:1793-5245
Container-title:International Journal of Biomathematics
language:en
Short-container-title:Int. J. Biomath.

Author:

Ouyang Miao¹,Zhang Yongping¹^ORCID,Liu Jian²

Affiliation:

1. School of Mathematics and Statistics, Shandong University, Weihai, Weihai, Shandong 264209, P. R. China

2. School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, P. R. China

Abstract

It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set. In this paper, Julia set of the discrete version of the SIRS model is established to analyze the fractal dynamics of this model. Then, controller is designed to change the Julia set. Furthermore, the box-counting dimensions of the controlled Julia sets by selecting different appropriate parameters are computed to show the complexity of the model. Finally, a nonlinear coupling method is introduced to synchronize the Julia sets with different parameters of the same system. Simulation results show the efficacy of these methods.

Funder

National Natural Science Foundation of China -Shandong

Natural Science Foundation of Shandong Province

Fundamental Research Funds for the Central Universities

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793524519500852

Reference25 articles.