Fractal Control and Synchronization of the Discrete Fractional SIRS Model

Fractal Control and Synchronization of the Discrete Fractional SIRS Model

SIRS model is one of the most basic models in the dynamic warehouse model of infectious diseases, which describes the temporary immunity after cure. The discrete SIRS models with the Caputo deltas sense and the theories of fractional calculus and fractal theory provide a reasonable and sensible pers...

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Main Authors: Miao Ouyang, Yongping Zhang, Jian Liu
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/3085036
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spelling doaj-9bc503280c3842dfaba30643bf5737602020-11-25T00:11:19ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/30850363085036Fractal Control and Synchronization of the Discrete Fractional SIRS ModelMiao Ouyang0Yongping Zhang1Jian Liu2School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, ChinaSchool of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, ChinaSchool of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, ChinaSIRS model is one of the most basic models in the dynamic warehouse model of infectious diseases, which describes the temporary immunity after cure. The discrete SIRS models with the Caputo deltas sense and the theories of fractional calculus and fractal theory provide a reasonable and sensible perspective of studying infectious disease phenomenon. After discussing the fixed point of the fractional order system, controllers of Julia sets are designed by utilizing fixed point, which are introduced as a whole and a part in the models. Then, two totally different coupled controllers are introduced to achieve the synchronization of Julia sets of the discrete fractional order systems with different parameters but with the same structure. And new proofs about the synchronization of Julia sets are given. The complexity and irregularity of Julia sets can be seen from the figures, and the correctness of the theoretical analysis is exhibited by the simulation results.http://dx.doi.org/10.1155/2020/3085036
collection DOAJ
language English
format Article
sources DOAJ
author Miao Ouyang
Yongping Zhang
Jian Liu
spellingShingle Miao Ouyang
Yongping Zhang
Jian Liu
Fractal Control and Synchronization of the Discrete Fractional SIRS Model
Complexity
author_facet Miao Ouyang
Yongping Zhang
Jian Liu
author_sort Miao Ouyang
title Fractal Control and Synchronization of the Discrete Fractional SIRS Model
title_short Fractal Control and Synchronization of the Discrete Fractional SIRS Model
title_full Fractal Control and Synchronization of the Discrete Fractional SIRS Model
title_fullStr Fractal Control and Synchronization of the Discrete Fractional SIRS Model
title_full_unstemmed Fractal Control and Synchronization of the Discrete Fractional SIRS Model
title_sort fractal control and synchronization of the discrete fractional sirs model
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
description SIRS model is one of the most basic models in the dynamic warehouse model of infectious diseases, which describes the temporary immunity after cure. The discrete SIRS models with the Caputo deltas sense and the theories of fractional calculus and fractal theory provide a reasonable and sensible perspective of studying infectious disease phenomenon. After discussing the fixed point of the fractional order system, controllers of Julia sets are designed by utilizing fixed point, which are introduced as a whole and a part in the models. Then, two totally different coupled controllers are introduced to achieve the synchronization of Julia sets of the discrete fractional order systems with different parameters but with the same structure. And new proofs about the synchronization of Julia sets are given. The complexity and irregularity of Julia sets can be seen from the figures, and the correctness of the theoretical analysis is exhibited by the simulation results.
url http://dx.doi.org/10.1155/2020/3085036
work_keys_str_mv AT miaoouyang fractalcontrolandsynchronizationofthediscretefractionalsirsmodel
AT yongpingzhang fractalcontrolandsynchronizationofthediscretefractionalsirsmodel
AT jianliu fractalcontrolandsynchronizationofthediscretefractionalsirsmodel
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