Synchronization in Fractional-Order Delayed Non-Autonomous Neural Networks
Abstract
:1. Introduction
2. Preliminaries and System Description
3. Main Conclusions and Their Proof
4. Numerical Simulation
5. Summary and Future Work
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Song, Q. Synchronization analysis of coupled connected neural networks with mixed time delays. Neurocomputing 2009, 72, 3907–3914. [Google Scholar] [CrossRef]
- Bao, H.; Park, J.H.; Cao, J. Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn. 2015, 82, 1343–1354. [Google Scholar] [CrossRef]
- Velmurugan, G.; Rakkiyappan, R.; Cao, J. Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Netw. 2016, 73, 36–46. [Google Scholar] [CrossRef] [PubMed]
- Gu, Y.; Yu, Y.; Wang, H. Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty. J. Frankl. Inst. 2016, 353, 3657–3684. [Google Scholar] [CrossRef]
- Stamova, I.; Stamov, G. Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction–diffusion terms using impulsive and linear controllers. Neural Netw. 2017, 96, 22–32. [Google Scholar] [CrossRef] [PubMed]
- Hu, H.-P.; Wang, J.-K.; Xie, F.-L. Dynamics analysis of a new fractional-order hopfield neural network with delay and its generalized projective synchronization. Entropy 2019, 21, 1. [Google Scholar] [CrossRef] [PubMed]
- Zhang, W.; Cao, J.; Wu, R.; Alsaedi, A.; Alsaadi, F.E. Projective synchronization of fractional-order delayed neural networks based on the comparison principle. Adv. Differ. Equ. 2018, 2018, 73. [Google Scholar] [CrossRef]
- Yu, J.; Hu, C.; Jiang, H.; Fan, X. Projective synchronization for fractional neural networks. Neural Netw. 2014, 49, 87–95. [Google Scholar] [CrossRef] [PubMed]
- Hu, T.; Zhang, X.; Zhong, S. Global asymptotic synchronization of nonidentical fractional-order neural networks. Neurocomputing 2018, 313, 39–46. [Google Scholar] [CrossRef]
- Wang, H.; Yu, Y.; Wen, G.; Zhang, S. Stability analysis of fractional-order neural networks with time delay. Neural Process. Lett. 2015, 42, 479–500. [Google Scholar] [CrossRef]
- Peng, X.; Wu, H.; Song, K.; Shi, J. Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Neural Netw. 2017, 94, 46–54. [Google Scholar] [CrossRef] [PubMed]
- Zhang, L.; Yang, Y.; Wang, F. Synchronization analysis of fractional-order neural networks with time-varying delays via discontinuous neuron activations. Neurocomputing 2018, 275, 40–49. [Google Scholar] [CrossRef]
- Yang, X.; Li, C.; Huang, T.; Song, Q.; Huang, J. Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays. Chaos Solitons Fractals 2018, 110, 105–123. [Google Scholar] [CrossRef]
- Wang, C.; Yang, Q.; Zhuo, Y.; Li, R. Synchronization analysis of a fractional-order non-autonomous neural network with time delay. Phys. A Stat. Mech. Its Appl. 2020, 549, 124176. [Google Scholar] [CrossRef]
- Wang, C.; Lei, Z.; Jia, L.; Du, Y.; Zhang, Q.; Liu, J. Projective synchronization of a nonautonomous delayed neural networks with Caputo derivative. Int. J. Biomath. 2024, 17, 2350069. [Google Scholar] [CrossRef]
- Pldlubny, I. Fractional Differential Equations; Academic Press: San Diego, CA, USA, 1999. [Google Scholar]
- Anatoly, A.K.; Hari, M.S.; Juan, J.T. Theory and Applications of Fractional Differential Equations; Elsevier Science Ltd.: New York, NY, USA, 2006. [Google Scholar]
- Duarte-Mermoud, M.A.; Aguila-Camacho, N.; Gallegos, J.A.; Castro-Linares, R. Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 2015, 22, 650–659. [Google Scholar] [CrossRef]
- Chen, B.; Chen, J. Razumikhin-type stability theorems for functional fractional-order differential systems and applications. Appl. Math. Comput. 2015, 254, 63–69. [Google Scholar] [CrossRef]
- Dass, A.; Srivastava, S.; Kumar, R. A novel Lyapunov-stability-based recurrent-fuzzy system for the Identification and adaptive control of nonlinear systems. Appl. Soft Comput. 2023, 137, 110161. [Google Scholar] [CrossRef]
- Man, Z.; Wu, H.R.; Liu, S.; Yu, X. A new adaptive backpropagation algorithm based on lyapunov stability theory for neural networks. IEEE Trans. Neural Netw. 2006, 17, 1580–1591. [Google Scholar] [CrossRef] [PubMed]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the authors. 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/).
Share and Cite
Wu, D.; Wang, C.; Jiang, T. Synchronization in Fractional-Order Delayed Non-Autonomous Neural Networks. Mathematics 2025, 13, 1048. https://doi.org/10.3390/math13071048
Wu D, Wang C, Jiang T. Synchronization in Fractional-Order Delayed Non-Autonomous Neural Networks. Mathematics. 2025; 13(7):1048. https://doi.org/10.3390/math13071048
Chicago/Turabian StyleWu, Dingping, Changyou Wang, and Tao Jiang. 2025. "Synchronization in Fractional-Order Delayed Non-Autonomous Neural Networks" Mathematics 13, no. 7: 1048. https://doi.org/10.3390/math13071048
APA StyleWu, D., Wang, C., & Jiang, T. (2025). Synchronization in Fractional-Order Delayed Non-Autonomous Neural Networks. Mathematics, 13(7), 1048. https://doi.org/10.3390/math13071048