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Optimal control and bifurcation diagram for a model nonlinear fractional SIRC
In this article, the optimal control for nonlinear SIRC model is studied in fractional order using the Caputo fractional derivative. Graph signal flow is given of the model and simulated by Simulink/Matlab which helps in discussing the topological structure of the model. Dynamics of the system versu...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7324937/ http://dx.doi.org/10.1016/j.aej.2020.05.028 |
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author | Mahdy, A.M.S. Higazy, M. Gepreel, K.A. El-dahdouh, A.A.A. |
author_facet | Mahdy, A.M.S. Higazy, M. Gepreel, K.A. El-dahdouh, A.A.A. |
author_sort | Mahdy, A.M.S. |
collection | PubMed |
description | In this article, the optimal control for nonlinear SIRC model is studied in fractional order using the Caputo fractional derivative. Graph signal flow is given of the model and simulated by Simulink/Matlab which helps in discussing the topological structure of the model. Dynamics of the system versus certain parameters are studied via bifurcation diagrams, Lyapunov exponents and Poincare maps. The existence of a uniformly stable solution is proved after control. The obtained results display the activeness and suitability of the Mittag Generalized-Leffler function method (MGLFM). The approximate solution of the fractional order SIRC model using MGLFM is explained by giving the figures of solutions before and after control. Also, we plot the 3D relationships with different alpha (fractional order) which display the originality and suitability of the results. |
format | Online Article Text |
id | pubmed-7324937 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. |
record_format | MEDLINE/PubMed |
spelling | pubmed-73249372020-06-30 Optimal control and bifurcation diagram for a model nonlinear fractional SIRC Mahdy, A.M.S. Higazy, M. Gepreel, K.A. El-dahdouh, A.A.A. Alexandria Engineering Journal Article In this article, the optimal control for nonlinear SIRC model is studied in fractional order using the Caputo fractional derivative. Graph signal flow is given of the model and simulated by Simulink/Matlab which helps in discussing the topological structure of the model. Dynamics of the system versus certain parameters are studied via bifurcation diagrams, Lyapunov exponents and Poincare maps. The existence of a uniformly stable solution is proved after control. The obtained results display the activeness and suitability of the Mittag Generalized-Leffler function method (MGLFM). The approximate solution of the fractional order SIRC model using MGLFM is explained by giving the figures of solutions before and after control. Also, we plot the 3D relationships with different alpha (fractional order) which display the originality and suitability of the results. The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. 2020-10 2020-06-30 /pmc/articles/PMC7324937/ http://dx.doi.org/10.1016/j.aej.2020.05.028 Text en © 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active. |
spellingShingle | Article Mahdy, A.M.S. Higazy, M. Gepreel, K.A. El-dahdouh, A.A.A. Optimal control and bifurcation diagram for a model nonlinear fractional SIRC |
title | Optimal control and bifurcation diagram for a model nonlinear fractional SIRC |
title_full | Optimal control and bifurcation diagram for a model nonlinear fractional SIRC |
title_fullStr | Optimal control and bifurcation diagram for a model nonlinear fractional SIRC |
title_full_unstemmed | Optimal control and bifurcation diagram for a model nonlinear fractional SIRC |
title_short | Optimal control and bifurcation diagram for a model nonlinear fractional SIRC |
title_sort | optimal control and bifurcation diagram for a model nonlinear fractional sirc |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7324937/ http://dx.doi.org/10.1016/j.aej.2020.05.028 |
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