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带有比例时滞的分数阶双向联想记忆神经网络的有限时间稳定
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Abstract:
本文研究了一类带有比例时滞的分数阶双向联想记忆神经网络的有限时间稳定性。基于一个新的广义Gronwall不等式，导出了阶数在0到1之间的分数阶系统的有限时间稳定的条件。最后通过数值仿真验证了所得条件的有效性。
This paper focuses on the finite-time stability for a class of fractional-order bidirectional associative memory neural networks with proportional delay. Based on new generalized Gronwall inequality, a criterion is obtained to realize the finite-time stability of systems when the fractional order is be-tween 0 and 1. Finally, the effectiveness of our criteria is supported by a numerical example.
| [1] | Kosko, B. (1988) Bidirectional Associative Memories. IEEE Transactions on Systems, Man, and Cybernetics, 18, 49-60. https://doi.org/10.1109/21.87054 |
| [2] | Acevedo-Mosqueda, M., Yanez-Marquez, C. and Lopez-Yanez, I. (2007) Alpha-Beta Bidirectional Associative Memories: Theory and Applications. Neural Processing Letters, 26, 1-40. https://doi.org/10.1007/s11063-007-9040-2 |
| [3] | Balasubramaniam, P. and Vembarasan, V. (2011) Asymptotic Stability of BAM Neural Networks of Neutral-Type with Impulsive Effects and Time Delay in the Leakage Term. Inter-national Journal of Computer Mathematics, 88, 3271-3291. https://doi.org/10.1080/00207160.2011.591388 |
| [4] | Huang, B.D. and Cao, J.D. (2018) Impact of Leakage Delay on Bifurcation in High-Order Fractional BAM Neural Networks. Neural Networks, 98, 223-235. https://doi.org/10.1016/j.neunet.2017.11.020 |
| [5] | Hansan, S. and Siong, N. (1997) A Parallel Processing VLSI BAM Engine. IEEE Transactions on Neural Networks, 8, 424-436. https://doi.org/10.1109/72.557697 |
| [6] | Cui, N., Jiang, H.J., Hu, C. and Abdurahman, A. (2018) Global Asymptotic and Robust Stability of Inertial Neural Networks with Proportional Delays. Neurocomputing, 272, 326-333. https://doi.org/10.1016/j.neucom.2017.07.001 |
| [7] | Zhang, W.L., Li, C.D., Yang, S.J. and Yang, X.S. (2018) Syn-chronization Criteria for Neural Networks with Proportional Delays via Quantized Control. Nonlinear Dynamics, 94, 541-551. https://doi.org/10.1007/s11071-018-4376-x |
| [8] | Dovrolis, C., Stiliadis, D. and Ramanathan, P. (2022) Proportional Differentiated Services: Delay Differentiation and Packet Scheduling. IEEE/ACM Transactions on Net-working, 10, 12-26. https://doi.org/10.1109/90.986503 |
| [9] | Zhang, S., Yu, Y. and Yu, J. (2017) LMI Conditions for Global Stability of Fractional-Order Neural Networks. IEEE Transactions on Neural Networks and Learning Sys-tems, 28, 2423-2433.
https://doi.org/10.1109/TNNLS.2016.2574842 |
| [10] | Ding, Z., Zeng, Z. and Wang, L. (2018) Robust Finite-Time Stabilization of Fractional-Order Neural Networks with Discontinuous and Continuous Activation Functions under Un-certainty. IEEE Transactions on Neural Networks and Learning Systems, 29, 1477-1490. https://doi.org/10.1109/TNNLS.2017.2675442 |
| [11] | Du, F. and Lu, J. (2020) Finite-Time Stability of Neutral Frac-tional Order Time Delay Systems with Lipschitz Nonlinearities. Applied Mathematics and Computation, 375, Article ID: 125079. https://doi.org/10.1016/j.amc.2020.125079 |
| [12] | Wu, R., Hei, X. and Chen, L. (2013) Finite-Time Stability of Fractional-Order Neural Networks with Delay. Communications in Theoretical Physics, 60, 189-193. https://doi.org/10.1088/0253-6102/60/2/08 |
| [13] | Xu, C. and Li, P. (2019) On Finite-Time Stability for Fraction-al-Order Neural Networks with Proportional Delays. Neural Processing Letters, 50, 1241-1256. https://doi.org/10.1007/s11063-018-9917-2 |
| [14] | Syed Ali, M., Narayanan, G., Orman, Z., Shekher, V. and Arik, S. (2020) Finite Time Stability Analysis of Fractional-Order Complex-Valued Memristive Neural Networks with Propor-tional Delays. Neural Processing Letters, 51, 407-426. https://doi.org/10.1007/s11063-019-10097-7 |
| [15] | Podlubny, I. (1999) Fractional Differential Equations. Academic Press, New York. |
| [16] | Kilbas, A.A., Srivastava, H.M. and Trujil-lo, J.J. (2006) Theory and Application of Fractional Differential Equations. Elsevier, New York. |
| [17] | Kuczma, M. (2009) An Introduction to the Theory of Functional Equations and Inequalities: Cauthy’s Equation and Jensen’s Inequality. Birkh Birkh？useruser, Boston. https://doi.org/10.1007/978-3-7643-8749-5 |
| [18] | Yang, Z., Zhang, J., Hu, J. and Mei, J. (2021) New Results on Finite-Time Stability for Fractional-Order Neural Networks with Proportional Delay. Neurocomputing, 442, 327-336. https://doi.org/10.1016/j.neucom.2021.02.082 |
