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Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued ne...

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Autores principales: Kang, Qiaokun, Yang, Qingxi, Yang, Jing, Gan, Qintao, Li, Ruihong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9601584/
https://www.ncbi.nlm.nih.gov/pubmed/37420480
http://dx.doi.org/10.3390/e24101460
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author Kang, Qiaokun
Yang, Qingxi
Yang, Jing
Gan, Qintao
Li, Ruihong
author_facet Kang, Qiaokun
Yang, Qingxi
Yang, Jing
Gan, Qintao
Li, Ruihong
author_sort Kang, Qiaokun
collection PubMed
description The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts’ absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.
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spelling pubmed-96015842022-10-27 Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method Kang, Qiaokun Yang, Qingxi Yang, Jing Gan, Qintao Li, Ruihong Entropy (Basel) Article The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts’ absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation. MDPI 2022-10-13 /pmc/articles/PMC9601584/ /pubmed/37420480 http://dx.doi.org/10.3390/e24101460 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kang, Qiaokun
Yang, Qingxi
Yang, Jing
Gan, Qintao
Li, Ruihong
Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method
title Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method
title_full Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method
title_fullStr Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method
title_full_unstemmed Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method
title_short Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method
title_sort synchronization in finite-time of delayed fractional-order fully complex-valued dynamical networks via non-separation method
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9601584/
https://www.ncbi.nlm.nih.gov/pubmed/37420480
http://dx.doi.org/10.3390/e24101460
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