Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks
Abstract
1. Introduction
- We present a novel controller to establish a sufficient condition for reaching FXT and PDT synchronizations in fractional-order impulsive neural networks with diffusion terms.
- We establish the robustness of the FXT and PDT synchronization approaches against fluctuations in parameter configurations.
- We demonstrate the influence of the fractional-order parameter on the synchronization of the given system.
2. Preliminaries
2.1. Theoretical Background
- Riemann–Liouville integral for :
- Riemann–Liouville derivative for :
- Caputo derivative:
2.2. System Description
- (i)
- Lyapunov stable. For any , there is a such that for any and ;
- (ii)
- Finite-time convergence. There exists a function , called the settling time (ST) function, such that and for all ;
- (iii)
- is bounded. There exist such that for all .
- (i)
- , ;
- (ii)
2.3. Fractional-Order Lyapunov Exponent
3. Main Results
3.1. FXT Synchronization
3.2. PDT Synchronization
4. Numerical Examples
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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0.9631 | 0.3146 | 0.0073 | 1.2633 | −2.8999 | 1.4399 | −1.133 | −1.9869 | 2.977 | 3.0862 |
0.9631 | 0.3146 | 2.6592 | 0.2561 | 1.3996 | −2.2743 | −0.5121 | −2.0131 | −3.4819 | 2.2811 |
0.9631 | 0.3146 | 3.0266 | 1.7172 | 1.4111 | −1.7352 | −3.923 | −1.2189 | −0.1094 | −2.8969 |
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Mahemuti, R.; Abdurahman, A.; Muhammadhaji, A. Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks. Fractal Fract. 2025, 9, 88. https://doi.org/10.3390/fractalfract9020088
Mahemuti R, Abdurahman A, Muhammadhaji A. Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks. Fractal and Fractional. 2025; 9(2):88. https://doi.org/10.3390/fractalfract9020088
Chicago/Turabian StyleMahemuti, Rouzimaimaiti, Abdujelil Abdurahman, and Ahmadjan Muhammadhaji. 2025. "Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks" Fractal and Fractional 9, no. 2: 88. https://doi.org/10.3390/fractalfract9020088
APA StyleMahemuti, R., Abdurahman, A., & Muhammadhaji, A. (2025). Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks. Fractal and Fractional, 9(2), 88. https://doi.org/10.3390/fractalfract9020088