S-型分布时滞中立型神经网络稳定性
Stability of Neutral Neural Networks with S-Type Distributed Delays
摘要: 本文研究了一类具有S-型分布时滞的中立型神经网络的全局渐近稳定性问题。首先利用同胚映射理论证明系统平衡点的存在唯一性。然后构造Lyapunov-Krasovskii泛函，利用不等式方法得到新的稳定性代数判据。最后，通过两个数值例子并运用MATLAB仿真验证了新判据的有效性。
Abstract: In this paper, the global asymptotic stability of a class of neutral neural networks with S-type distributed delays is studied. Firstly, the existence and uniqueness of the equilibrium point of the system are proved by using the homeomorphic mapping theory. Secondly, by constructing an appropriate Lyapunov-Krasovskii functional and using the inequality method, a new algebraic criterion of stability is obtained. Finally, the effectiveness of the new criterion is proved by two numerical examples and MATLAB simulation.
文章引用：王冰, 孙小淇. S-型分布时滞中立型神经网络稳定性[J]. 理论数学, 2022, 12(4): 580-589. https://doi.org/10.12677/PM.2022.124065

参考文献

[1] Tamura, H., Zhang, Z., Xu, X.S., Ishii, M. and Tang, Z. (2005) Lagrangian Object Relaxation Neural Network for Combinatorial Optimization Problems. Neurocomputing, 68, 297-305. [Google Scholar] [CrossRef] 
[2] Calabuig, D., Monserrat, J.F., Gmez-Barquero, D. and Lzaro, O. (2008) An Efficient Dynamic Resource Allocation Algorithm for Packet-Switched Communication Networks Based on Hopfield Neural Excitation Method Original Research Article. Neurocomputing, 71, 3439-3446. [Google Scholar] [CrossRef] 
[3] Sammouda, R., Adgaba, N., Touir, A. and Al-Ghamdi, A. (2014) Agriculture Satellite Image Segmentation Using a Modified Artificial Hopfield Neural Network Original Research Article. Computers in Human Behavior, 30, 436-441. [Google Scholar] [CrossRef] 
[4] Kolmanovskii, V.B. and Nosov, V.R. (1986) Stability of Functional Differential Equations. Elsevier, London.
[5] Kuang, Y. (1993) Delay Differential Equations: With Applications in Population Dynamics. Elsevier, Boston.
[6] Niculescu, S.I. (2001) Delay Effects Stability: A Robust Control Approach. Springer, Berlin.
[7] Pauwels, R., Peng, W.L., Wu, Q.X. and Zhang, Z.Q. (2016) LMI-Based Global Ex-ponential Stability of Equilibrium Point for Neutral Delayed BAM Neural Networks with Delays in Leakage Terms via New Inequality Technique. Neurocomputing, 199, 103-113. [Google Scholar] [CrossRef] 
[8] Samli, R., Senan, S., Yucel, E. and Orman, Z. (2019) Some Generalized Global Stability Criteria for Delayed Cohen-Grossberg Neural Networks of Neutral-Type. Neural Networks, 116, 198-207. [Google Scholar] [CrossRef] [PubMed]
[9] Faydasicok, O. (2020) New Criteria for Global Stability of Neutral-Type Cohen-Grossberg Neural Networks with Multiple Delays. Neural Networks, 125, 330-337. [Google Scholar] [CrossRef] [PubMed]
[10] Popa, C.A. (2020) Global μ-Stability of Neutral-Type Impulsive Complex-Valued BAM Neural Networks with Leakage Delay and Unbounded Time-Varying Delays. Neurocomputing, 376, 73-94. [Google Scholar] [CrossRef] 
[11] Wan, L. and Zhou, Q.H. (2021) Exponential Stability of Neu-tral-Type Cohen-Grossberg Neural Networks with Multiple Time-Varying Delays. IEEE Access, 9, 48914-48922. [Google Scholar] [CrossRef] 
[12] Zhang, G.B., Wang, T., Li, T. and Fei, S.M. (2018) Multiple Integral Lyapunov Approach to Mixed-Delay-Dependent Stability of Neutral Neural Networks. Neurocomputing, 275, 1782-1792. [Google Scholar] [CrossRef] 
[13] Arik, S. (2020) New Criteria for Stability of Neutral-Type Neural Networks with Multiple Time Delays. IEEE Transactions on Neural Networks and Learning Systems, 31, 1504-1513. [Google Scholar] [CrossRef] 
[14] Wang, L.S. and Xu, D.Y. (2002) Global Asymp-totic Stability of Bidirectional Associative Memory Neural Networks with S-Type Distributed Delays. International Journal of System Science, 33, 869-877. [Google Scholar] [CrossRef] 
[15] Liu, P.C., Yi, F.Q., Guo, Q., Yang, J. and Wu, W. (2008) Analysis on Global Exponential Robust Stability of Reaction-Diffusion Neural Networks with S-Type Distributed De-lays. Physica D, 237, 475-485. [Google Scholar] [CrossRef] 
[16] Zhang, R.J. and Wang, L.S. (2009) Global Exponential Robust Stability of Interval Cellular Neural Networks with S-Type Distributed Delays. Mathematical and Computer Modelling, 50, 380-385. [Google Scholar] [CrossRef] 
[17] Huang, Z.K., Li, X.Z., Mohamad, S. and Lu, Z.Y. (2009) Robust Stability Analysis of Static Neural Network with S-Type Distributed Delays. Applied Mathematical Modelling, 33, 760-769. [Google Scholar] [CrossRef] 
[18] Wang, Y.F., Lu, C.G., Ji, G.R. and Wang, L.S. (2011) Global Exponential Stability of High-Order Hopfield-Type Neural Networks with S-Type Distributed Time Delays. Communications in Nonlinear Science and Numerical Simulation, 16, 3319-3325. [Google Scholar] [CrossRef] 
[19] Yao, Q., Wang, L.S. and Wang, Y.F. (2018) Exist-ence-Uniqueness and Stability of Reaction-Diffusion Stochastic Hopfield Neural Networks with S-Type Distributed Time Delays. Neurocomputing, 275, 470-477. [Google Scholar] [CrossRef] 

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