Abstract
By introducing appropriate stochastic factors into the neural networks, there were results showing that the neural networks can be stabilized. In this paper, stochastic stabilization of delayed neural networks is studied. First, a new type Razumikhin-type theorem about stochastic functional differential equations is proposed and the rigid proof is given by using Itô formula, Borel-Contelli lemma etc.. As a corollary of the theorem, a new type Razumikhin-type theorem of delayed stochastic differential equation is obtained. Next, taking the results obtained in the first section as the theoretic basis, the stabilization of the delayed deterministic neural networks is examined. The result obtained in the paper shows that the neural networks can be stabilized so long as the intensity of the random perturbation is large enough. The expression of the random intensity is presented which is convenient to networks’ design.
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References
Mao, X.: Stochastic Differential Equations and Applications. Horwood Pub., Chichester (1997)
Hale, J.K.: Theory of Functional Differential Equations. Springer, Heidelberg (1977)
Liao, W., Liao, X.: Robust Stability of Time-Delayed Interval CNN in Noisy Environment. Acta Automatica Sinica 30(2), 300–305 (2004)
Liao, X.: Stability Theory and Applications on Power Systems. Press of Defence Industry, Beijing (2000)
Liu, Y., Feng, Z.: Theory and Applications on Large-scale Dynamic Systems-Randomicity, Stability and Control. Press of South China University of Technology, Guangzhou (1992)
Zeng, Z., Wang, J., Liao, X.: Global Asymptotic Stability and Global Exponential Stability of Neural Networks with Unbounded Time-Varying delays. IEEE Trans. on Circuits and Systems II, Express Briefs 52(3), 168–173 (2005)
Mao, X.: Stochastic Stability and Stabilization. In: Proceedings of the 2002 International Conference on Control and Automation, Xiamen, China, pp. 1208–1212 (2002)
Mao, X.: Razumikhin-Type Theorems on Exponential Stability of Stochastic Functional Differential Equations. Stochastic Processes and Their Applications 65, 233–250 (1996)
Hopfield, J.J.: Neural Networks and Physical Systems with Emergent Collective Computational Abilityes. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)
Hopfield, J.J.: Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state Neurons. Proc. Natl. Acad. Sci. USA 81, 3088–3092 (1984)
Deng, F., Feng, Z., Liu, Y.: Stability and Feedback-stabilization of General Linear Delayed Systems. Control Theory and Application 15(2), 299–303 (1998)
Shen, Y., Liao, X.: Exponential Stability of Delayed Hopfield Neural Networks. Acta Mathematica Scientia 19(2), 211–218 (1999)
Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of Neural Networks with Time-Varying Delays. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 50(10), 1353–1358 (2003)
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Liao, W., Chen, J., Xu, Y., Liao, X. (2007). Stochastic Stabilization of Delayed Neural Networks. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72395-0_22
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DOI: https://doi.org/10.1007/978-3-540-72395-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72394-3
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