Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization
Research in the field of dynamic behaviors in neural networks with variable-order differences is currently a thriving area, marked by various significant discoveries. However, when it comes to discrete-time neural networks featuring fractional variable-order nonlocal and nonsingular kernels, there h...
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| Published in | The European physical journal. ST, Special topics Vol. 234; no. 9; pp. 2761 - 2774 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1951-6355 1951-6401 |
| DOI | 10.1140/epjs/s11734-024-01167-6 |
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| Abstract | Research in the field of dynamic behaviors in neural networks with variable-order differences is currently a thriving area, marked by various significant discoveries. However, when it comes to discrete-time neural networks featuring fractional variable-order nonlocal and nonsingular kernels, there has been limited exploration. This paper stands as one of the initial contributions to this subject, focusing primarily on the topics of stability and synchronization in finite-time within discrete neural networks. The research employs the nabla ABC variable-order difference operator, with a primary approach involving the investigation of a novel Gronwall inequality using the Atangana-Baleanu difference variable-order sum operator. This analysis leads to the development of a uniqueness theorem and a criterion for the stability in finite-time of variable-order discrete neural networks. Furthermore, the requirements stemming from this type of stability and the novel Gronwall inequality serve as the foundation for establishing the conditions necessary for achieving finite-time synchronization in these networks, employing a specific control using state feedback method. Finally, the study utilizes numerical solutions to validate the obtained results. |
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| AbstractList | Research in the field of dynamic behaviors in neural networks with variable-order differences is currently a thriving area, marked by various significant discoveries. However, when it comes to discrete-time neural networks featuring fractional variable-order nonlocal and nonsingular kernels, there has been limited exploration. This paper stands as one of the initial contributions to this subject, focusing primarily on the topics of stability and synchronization in finite-time within discrete neural networks. The research employs the nabla ABC variable-order difference operator, with a primary approach involving the investigation of a novel Gronwall inequality using the Atangana-Baleanu difference variable-order sum operator. This analysis leads to the development of a uniqueness theorem and a criterion for the stability in finite-time of variable-order discrete neural networks. Furthermore, the requirements stemming from this type of stability and the novel Gronwall inequality serve as the foundation for establishing the conditions necessary for achieving finite-time synchronization in these networks, employing a specific control using state feedback method. Finally, the study utilizes numerical solutions to validate the obtained results. |
| Author | Ouannas, Adel Grassi, Giuseppe Hioual, Amel Al-Tarawneh, Hassan Alomari, Saleh |
| Author_xml | – sequence: 1 givenname: Amel orcidid: 0000-0001-6944-1689 surname: Hioual fullname: Hioual, Amel email: amel.hioual@univ-oeb.dz organization: Laboratory of Dynamical Systems and Control, University of Oum El-Bouaghi – sequence: 2 givenname: Saleh surname: Alomari fullname: Alomari, Saleh organization: Faculty of Science and Information Technology, Software Engineering, Jadara University – sequence: 3 givenname: Hassan surname: Al-Tarawneh fullname: Al-Tarawneh, Hassan organization: Department of Data Sciences and Artificial Intelligence, Al-Ahliyya Amman University – sequence: 4 givenname: Adel surname: Ouannas fullname: Ouannas, Adel organization: Department of Mathematics and Computer Science, University of Oum EL-Bouaghi – sequence: 5 givenname: Giuseppe surname: Grassi fullname: Grassi, Giuseppe organization: Dipartimento Ingegneria Innovazione, Universita del Salento |
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| SubjectTerms | Atomic Classical and Continuum Physics Condensed Matter Physics Discrete Neural Networks: Firing Patterns and Synchronization Strategies - Basics for New AI Technologies Finite differences Materials Science Measurement Science and Instrumentation Molecular Neural networks Operators (mathematics) Optical and Plasma Physics Physics Physics and Astronomy Regular Article Stability State feedback Time synchronization Uniqueness theorems |
| Title | Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization |
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