Abstract
In this paper, the global exponential stability in the mean square of stochastic Cohen-Grossberg neural networks (SCGNNS) with mixed delays is studied. By applying the Lyapunov function, stochastic analysis technique and inequality techniques, some sufficient conditions are obtained to ensure the exponential stability in the mean square of the SCGNNS. An example is given to illustrate the theoretical results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cohen, M., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems Man and Cybernetics 3, 815–826 (1983)
Oliveira, J.: Global stability of a Cohen-Grossberg neural network with both time-varying and continuous distributed delays. Nonlinear Analysis: Real World Applications 12, 2861–2870 (2011)
Wang, L.: Stability of Cohen-Grossberg neural networks with distributed delays. Applied Mathematics and Computation 160, 93–110 (2005)
Zhou, J., Zhao, W., Lv, X., Zhu, H.: Stability analysis of almost periodic solutions for delayed neural networks without global Lipschitz activation functions. Mathematics and Computers in Simulation 81, 2440–2445 (2011)
Zhang, Z., Liu, W., Zhou, D.: Global asymptotic stability to a generalized Cohen-Grossberg neural networks of neutral type delays. Neural Networks 25, 94–105 (2012)
Tojtovska, B., Janković, S.: On a general decay stability of stochastic Cohen-Grossberg neural networks with time-varying delays. Applied Mathematics and Computation 219, 2289–2302 (2012)
Balasubramaniam, P., Ali, M.: Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays. Mathematical and Computer Modelling 53, 151–160 (2011)
Li, L., Fang, Z., Yang, Y.: A shunting inhibitory cellular neural network with continuously distributed delays of neutral type. Nonlinear Analysis: Real World Applications 13, 1186–1196 (2012)
Mahmoud, M., Ismail, A.: Improved results on robust exponential stability criteria for neutral-type delayed neural networks. Applied Mathematics and Computation 217, 3011–3019 (2010)
Rakkiyappan, R., Balasubramaniam, P.: New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71, 1039–1045 (2008)
Zhu, Q., Li, X.: Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks. Fuzzy Sets and Systems 203, 74–79 (2012)
Li, D., He, D., Xu, D.: Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with delays. Mathematics and Computers in Simulation 82, 1531–1543 (2012)
Zhou, W., Wang, T., Mou, J., Fang, J.: Mean square exponential synchronization in Lagrange sense for uncertain complex dynamical networks. Journal of the Franklin Institute 349, 1267–1282 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liang, T., Yang, Y., Hu, M., Liu, Y., Li, L. (2013). Global Exponential Stability in the Mean Square of Stochastic Cohen-Grossberg Neural Networks with Time-Varying and Continuous Distributed Delays. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-39065-4_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39064-7
Online ISBN: 978-3-642-39065-4
eBook Packages: Computer ScienceComputer Science (R0)