A NEW CRITERION FOR STABILITY OF NEUTRAL-TYPE HOPFIELD NEURAL NETWORKS WITH CONSTANT DELAYS

Yıl 2020, Cilt: 25 Sayı: 2, 639 - 650, 31.08.2020

Özlem Faydasıçok

https://doi.org/10.17482/uumfd.716884

Öz

This paper makes some contributions to the stability problem of neutral-type Hopfield neural network model having a constant time delay in states of neurons and a constant neutral delay in the time derivatives of states of neurons. With the help of a suitable Lyapunov functional, a novel stability criterion is derived for neutral-type Hopfield neural network model. This stability criterion only requires to check the positive defineteness of the matrices involving the system elements of this type of neural networks. The presented stability condition proved to be independently of these time and neutral delays. Therefore, this condition can be easily justified by applying the properties of some certain matrices. A numerical example for this type of neutral systems is studied to show the applicability of the presented stability result. 

Anahtar Kelimeler

Neutral-Type Systems, Hopfield Neural Networks, Lyapunov Functionals, Stability Analysis

Sabit Gecikmeler İçeren Nötral-Tip Hopfield Yapay Sinir Ağlarının Kararlılığı için Yeni Bir Kriter

Öz

Bu makale, hem nöron durumlarının hem de nöron durumlarının türevlerinde sabit gecikmeler içeren nötral-tip Hopfield yapay sinir ağı modelinin kararlılık problemine yeni katkılar yapmaktadır. Uygun bir Lyapunov fonksiyoneli yardımıyla, nötral-tip Hopfield yapay sinir ağlarının kararlılığını sağlayan yeni bir kriter sunulmaktadır. Bu kararlılık kriterinin en önemli avantajı sadece sistem elemanlarından oluşan özel bir matrisin pozitif tanımlı olmasını test edilmesine dayandırılmış olmasıdır. Ayrıca, elde edilen kararlılık koşulu zaman ve nötral gecikmelerden bağımsızdır. Bu nedenle, elde edilen kararlılık kriterinin geçerliliği bazı özel matris özellikleri yardımıyla kolayca test edilebilir. Diğer yandan, önerilen kararlılık koşulunun uygulanabilirliğini göstermek amacıyla sayısal bir örnek verilmiştir.

Anahtar Kelimeler

Nötral-Tip Sistemler, Hopfield Sinir Ağları, Lyapunov Fonksiyonelleri, Kararlılık Analizi

Kaynakça

• 1. Akca, H., Covachev, V. ve Covacheva, Z. (2015) Global Asymptotic Stability of Cohen-Grossberg Neural Networks of Neutral Type, Journal of Mathematical Sciences, 205(6), 719-732. 10.1007/s10958-015-2278-8.
• 2. Arik, S. (2014a) New Criteria for Global Robust Stability of Delayed Neural Networks With Norm-Bounded Uncertainties, IEEE Transactions on Neural Networks and Learning Systems, 25(6), 1045-1052. 10.1109/TNNLS.2013.2287279.
• 3. Arik, S. (2014b) An Analysis of Stability of Neutral-Type Neural Systems with Constant Time Delays, Journal of the Franklin Institute, 351(11), 4949-4959. 10.1016/j.jfranklin.2014.08.013.
• 4. Chen, H., Zhang, Y. ve Hu, P. (2010) Novel Delay-Dependent Robust Stability Criteria for Neutral Stochastic Delayed Neural Networks, Neurocomputing, 73(13-15), 2554-25561. 10.1016/j.neucom.2010.06.003.
• 5. Cheng, C. J., Liao, T. L., Yan, J. J. ve Hwang, C. C. (2008) Globally Asymptotic Stability of a Class of Neutral-Type Neural Networks With Delays, IEEE Transactions on Systems, Man, and Cybernetics-PART B: Cybernetics, 36(5), 1191-1195. 10.1109/TSMCB.2006.874677.
• 6. Dharani, S., Rakkiyappan R. ve Cao, J. (2015) New Delay-Dependent Stability Criteria for Switched Hopfield Neural Networks of Neutral Type with Additive Time-Darying Delay Components, Neurocomputing, 151(2) 827-834. 10.1016/j.neucom.2014.10.014.
• 7. Ge, C., Hua, C. ve Guan, X. (2014) New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach, IEEE Transactions on Neural Networks and Learning Systems, 25(7), 1378-1383. 10.1109/TNNLS.2013.2285564.
• 8. Hopfield, J. (1982) Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proceedings of National Academy of Science, 79, 2554-2558.
• 9. Jian, J. ve Duan, L. (2020) Finite-Time Synchronization for Fuzzy Neutral-Type Inertial Neural Networks with Time-Varying Coefficients and Proportional Delays, Fuzzy Sets and Systems, 381, 51-67. 10.1016/j.fss.2019.04.004.
• 10. Kolmanovskii, V. B. ve Nosov, V. R. (1986) Stability of Functional Differential Equations, Academic Press, London.
• 11. Kuang, Y. (1993) Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston.
• 12. Lakshmanan, S., Park, J. H., Jung, H. Y., Kwon, O. M. ve Rakkiyappan, R. (2013) A Delay Partitioning Approach to Delay-Dependent Stability Analysis for Neutral Type Neural Networks with Discrete and Distributed Delays, Neurocomputing, 111, 81-89. 10.1016/j.neucom.2012.12.016.
• 13. Liao, X., Liu, Y., Wang, H. ve Huang, T. (2015) Exponential Estimates and Exponential Stability for Neutral-Type Neural Networks with Multiple Delays, Neurocomputing, 149(3), 868-883. 10.1016/j.neucom.2014.07.048.
• 14. Lien, C. H., Yu, K. W. , Lin, Y. F., Chung, Y. J. ve Chung, L. Y. (2008) Global Exponential Stability for Uncertain Delayed Neural Networks of Neutral Type With Mixed Time Delays, IEEE Transactions on Systems, Man, and Cybernetics-PART B: Cybernetics, 38(3), 709-720. 10.1109/TSMCB.2008.918564.
• 15. Manivannan, R., Samidurai, R., Cao, J., Alsaedi, A. ve E.Alsaadi, F. (2017) Global Exponential Stability and Dissipativity of Generalized Neural Networks with Time-Varying Delay Signals, Neural Networks, 87, 149-159. 10.1016/j.neunet.2016.12.005.
• 16. Manivannan, R., Panda, S., Chong, K. T. ve Cao, J. (2018) An Arcak-Type State Estimation Design for Time-Delayed Static Neural Networks with Leakage Term Based on Unified Criteria, Neural Networks, 106, 110-126. 10.1016/j.neunet.2018.06.015.
• 17. Muralisankar, S., Manivannan, A. ve Balasubramaniam, P. (2015) Mean Square Delay Dependent-Probability-Distribution Stability Analysis of Neutral Type Stochastic Neural Networks, ISA Transactions, 58, 11-19. 10.1016/j.isatra.2015.03.004.
• 18. Niculescu, S. I. (2001) Delay Effects on Stability: A Robust Control Approach, Springer, Berlin.
• 19. Orman, Z. (2012) New Sufficient Conditions for Global Stability of Neutral-Type Neural Networks with Time Delays, Neurocomputing, 97, 141-148. 10.1016/j.neucom.2012.05.016.
• 20. Ozcan, N. (2018) New Conditions for Global Stability of Neutral-Type Delayed Cohen-Grossberg Neural Networks, Neural Networks, 106, 1-7. 10.1016/j.neunet.2018.06.009.
• 21. Ozcan, N. (2019) Stability Analysis of Cohen–Grossberg Neural Networks of Neutral-Type: Multiple Delays Case, Neural Networks, 113, 20-27. 10.1016/j.neunet.2019.01.017.
• 22. Samli, R. ve Arik, S. (2009) New Results for Global Stability of a Class of Neutral-Type Neural Systems with Time Delays, Applied Mathematics and Computation, 210(2), 564-570. 10.1016/j.amc.2009.01.031.
• 23. Shi, K., Zhong, S., Zhu, H., Liu, X. ve Zeng, Y. (2015) New Delay-Dependent Stability Criteria for Neutral-Type Neural Networks with Mixed Random Time-Varying Delays, Neurocomputing, 168, 896-907. 10.1016/j.neucom.2015.05.035.
• 24. Shi, K., Zhu, H., Zhong, S., Zeng, Y. ve Zhang, Y. (2015) New Stability Analysis for Neutral Type Neural Networks with Discrete and Distributed Delays Using a Multiple Integral Approach, Journal of the Franklin Institute, 352(1), 155-176. 10.1016/j.jfranklin.2014.10.005.
• 25. Shu, J., Xiong, L., Wu, T. ve Liu, Z. (2019) Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay, Mathematics, 7, 1-23. 10.3390/math7010101.
• 26. Song, Q., Yu,Q., Zhao, Z., Liu, Y. ve Alsaadi, F. E. (2018) Boundedness and Global Robust Stability Analysis of Delayed Complex-Valued Neural Networks with Interval Parameter Uncertainties, Neural Networks, 103, 55-62. 10.1016/j.neunet.2018.03.008.
• 27. Tu, Z., Cao, J., Alsaedi, A., Alsaadi, F. E. ve Hayat, T. (2016) Global Lagrange Stability of Complex‐Valued Neural Networks of Neutral Type with Time‐Varying Delays, Complexity, 21, 438-450. 10.1002/cplx.21823.
• 28. Wang, J., Jiang, H., Ma, T. ve Hu, C. (2018) Delay-Dependent Dynamical Analysis of Complex-Valued Memristive Neural Networks: Continuous-Time and Discrete-Time Cases, Neural Networks, 101, 33-46. 10.1016/j.neunet.2018.01.015.
• 29. Yang, Y., Liang, T. ve Xu, X. (2015) Almost Sure Exponential Stability of Stochastic Cohen-Grossberg Neural Networks with Continuous Distributed Delays of Neutral Type, Optik – International Journal for Light and Electron Optics, 126(23), 4628-4635. 10.1016/j.ijleo.2015.08.099.
• 30. Zhang, C. K., He, Y., Jiang, L., Lin, W. J. ve Wu, M. (2017) Delay-Dependent Stability Analysis of Neural Networks with Time-Varying Delay: A Generalized Free-Weighting-Matrix Approach, Applied Mathematics and Computation, 294, 102-120. 10.1016/j.amc.2016.08.043.
• 31. Zhang, G., Wang, T., Li, T. ve Fei, S. (2018) Multiple Integral Lyapunov Approach to Mixed-Delay-Dependent Stability of Neutral Neural Networks, Neurocomputing, 275, 1782-1792. 10.1016/j.neucom.2017.10.021.
• 32. Zhu, Q. ve Cao, J. (2010) Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays, IEEE Transactions on Neural Networks, 21(8), 1314-1325. 10.1109/TNN.2010.2054108.