Abstract
The exponential stability is discussed for Cohen-Grossberg neural networks with discrete delays. Without assuming the boundedness, differentiability and monotonicity of the activation functions, the nonlinear measure approach is employed to analyze the existence and uniqueness of an equilibrium, and a novel Lyapunov functional is constructed to investigate the exponential stability of the networks. New general sufficient conditions, which are independent of the delays, are derived for the global exponential stability of the delayed neural networks.
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References
Chen, T.P., Rong, L.B.: Delay-Independent Stability Analysis of Cohen-Grossberg Neural Networks. Physics Letters A 317, 436–449 (2003)
Cohen, M.A., Grossberg, S.: Absolute Stability and Global Pattern Formation and Partial Memory Storage by Competitive Neural Networks. IEEE Transactions on Systems, Man and Cybernetics SMC-13, 815–826 (1983)
van den Driessche, P., Zou, X.: Global Attractivity in Delayed Hopfield Neural Network Models. SIAM J. Appl. Math. 58, 1878–1890 (1998)
Grossberg, S.: Nonlinear Neural Networks: Principles, Mechanisms, and Architechtures. Neural Networks 1, 17–61 (1988)
Liao, X.F., Li, C.G., Wong, K.W.: Criteria for Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 17, 1401–1414 (2004)
Marcus, C., Westervelt, R.: Stability of Analog Neural Networks with Delay. Physics Review A 39, 347–359 (1989)
Morita, M.: Associative Memory with Non-monotone Dynamics. Neural Networks 6(1), 115–126 (1993)
Peng, J.G., Qiao, H., Xu, Z.B.: A New Approach to Stability of Neural Networks with Time-Varying Delays. Neural Networks 15, 95–103 (2002)
Qiao, H., Peng, J.G., Xu, Z.B.: Nonlinear Measures: A New Approach to Exponential Stability Analysis for Hopfield-Type Neural Networks. IEEE Transactions on Neural Networks 12(2), 360–370 (2001)
Tank, D.W., Hopfield, J.J.: Simple “Neural” Optimization Networks: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit. IEEE Transactions on Circuits and Systems 33(5), 533–541 (1986)
Wan, A.H., Peng, J.G., Wang, M.S.: Exponential Stability of a Class of Generalized Neural Networks with Time-Varying Delays. Neurocomputing 69(7-9), 959–963 (2006)
Wan, A.H., Wang, M.S., Peng, J.G., Qiao, H.: Exponential Stability of Cohen-Grossberg Neural Networks with a General Class of Activation Functions. Physics Letters A 350(1-2), 96–102 (2006)
Wang, L., Zou, X.F.: Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 15, 415–422 (2002)
Wang, L., Zou, X.F.: Harmless Delays in Cohen-Grossberg Neural Network. Physica D 170(2), 162–173 (2002)
Ye, H., Michel, A.N., Wang, K.: Qualitative Analysis of Cohen-Grossberg Neural Networks with Multiple Delays. Physics Review E 51, 2611–2618 (1995)
Zhang, J.Y., Jin, X.S.: Global Stability Analysis in Delayed Hopfield Neural Network Models. Neural Networks 13, 745–753 (2000)
Zhou, L., Zhou, M.R.: Stability Analysis of a Class of Generalized Neural Networks with Delays. Physics Letters A 337, 203–215 (2005)
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Wan, A., Qiao, H., Zhang, B., Mao, W. (2006). New Results for Global Exponential Stability of Delayed Cohen-Grossberg Neural Networks. In: Huang, DS., Li, K., Irwin, G.W. (eds) Intelligent Computing. ICIC 2006. Lecture Notes in Computer Science, vol 4113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816157_48
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DOI: https://doi.org/10.1007/11816157_48
Publisher Name: Springer, Berlin, Heidelberg
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