Fractional-Order Degn–Harrison Reaction–Diffusion Model: Finite-Time Dynamics of Stability and Synchronization
This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criter...
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| Published in | Computation Vol. 12; no. 7; p. 144 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
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MDPI AG
01.07.2024
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| ISSN | 2079-3197 2079-3197 |
| DOI | 10.3390/computation12070144 |
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| Abstract | This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criteria, this lemma represents a significant extension of prior findings, laying the groundwork for subsequent investigations. Building upon this foundation, we proceed to develop efficient dependent linear controllers designed to orchestrate finite-time synchronization. Leveraging the power of a Lyapunov function, we derive new, robust conditions that ensure the attainment of synchronization within a predefined time frame. This innovative approach not only enhances our understanding of finite-time synchronization, but also offers practical solutions for its realization in complex systems. To validate the efficacy and applicability of our proposed methodology, extensive numerical simulations are conducted. Through this comprehensive analysis, we aim to contribute valuable insights to the field of fractional-order reaction–diffusion systems while paving the way for practical implementations in real-world applications. |
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| AbstractList | This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criteria, this lemma represents a significant extension of prior findings, laying the groundwork for subsequent investigations. Building upon this foundation, we proceed to develop efficient dependent linear controllers designed to orchestrate finite-time synchronization. Leveraging the power of a Lyapunov function, we derive new, robust conditions that ensure the attainment of synchronization within a predefined time frame. This innovative approach not only enhances our understanding of finite-time synchronization, but also offers practical solutions for its realization in complex systems. To validate the efficacy and applicability of our proposed methodology, extensive numerical simulations are conducted. Through this comprehensive analysis, we aim to contribute valuable insights to the field of fractional-order reaction–diffusion systems while paving the way for practical implementations in real-world applications. |
| Audience | Academic |
| Author | Bendib, Issam Alshanti, Waseem Ghazi Alshanty, Ahmad Hioual, Amel Ouannas, Adel Hammad, Ma’mon Abu Momani, Shaher |
| Author_xml | – sequence: 1 givenname: Ma’mon Abu surname: Hammad fullname: Hammad, Ma’mon Abu – sequence: 2 givenname: Issam surname: Bendib fullname: Bendib, Issam – sequence: 3 givenname: Waseem Ghazi surname: Alshanti fullname: Alshanti, Waseem Ghazi – sequence: 4 givenname: Ahmad surname: Alshanty fullname: Alshanty, Ahmad – sequence: 5 givenname: Adel surname: Ouannas fullname: Ouannas, Adel – sequence: 6 givenname: Amel orcidid: 0000-0001-6944-1689 surname: Hioual fullname: Hioual, Amel – sequence: 7 givenname: Shaher surname: Momani fullname: Momani, Shaher |
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| Cites_doi | 10.1186/s13661-019-1188-y 10.1016/j.neucom.2015.11.094 10.1109/ACCESS.2020.2993784 10.1016/j.cnsns.2014.01.022 10.1007/s11071-013-1177-0 10.3390/fractalfract7050347 10.1142/S0218348X22401454 10.1140/epjs/s11734-023-00911-8 10.1063/5.0170419 10.1007/BF00279718 10.1190/geo2019-0066.1 10.1155/2019/2832781 10.3390/math11030555 10.1186/s13662-021-03286-z 10.1140/epjst/e2020-900193-4 10.1007/s10543-014-0484-2 10.1016/j.mcm.2009.12.004 10.3390/fractalfract7110828 10.1140/epjst/e2020-900177-6 10.1007/s00009-017-0894-x 10.3390/axioms12080728 10.1007/s11538-006-9062-3 10.3390/fractalfract8040231 10.3390/axioms12090806 10.1016/j.chaos.2021.110698 10.1002/mma.6807 10.1016/j.camwa.2012.01.056 10.1137/S0036142900374111 |
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| SubjectTerms | Behavior Communications networks Complex systems Degn–Harrison reaction–diffusion systems Diffusion Dynamical systems Efficiency Equilibrium finite-time stability finite-time synchronization Liapunov functions Lyapunov function Mathematical functions Mathematical models Numerical analysis Partial differential equations Reaction-diffusion equations Robotics Stability Stability analysis Stability criteria Time dependence Time synchronization |
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| Title | Fractional-Order Degn–Harrison Reaction–Diffusion Model: Finite-Time Dynamics of Stability and Synchronization |
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