Global Exponential Stability Analysis for Cohen-Grossberg Neural Networks with Non-Lipschitz Neuron Activations

Hong Wen Xu

doi:10.4028/www.scientific.net/AMM.58-60.1136

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 58-60Global Exponential Stability Analysis for...

Global Exponential Stability Analysis for Cohen-Grossberg Neural Networks with Non-Lipschitz Neuron Activations

Abstract:

In this paper，a novel class of Cohen-Grossberg neural networks with inverse Hlder neuron activation functions is presented. By employing the Brouwer degree properties and linear matrix inequality techniques, the existence and uniqueness of equilibrium point for such Cohen-Grossberg neural networks are investigated. By constructing appropriate Lyapunov functions and using Lyapunov diagonally stable matrices, a sufficient condition which is used to checked the global exponential stability of a unique equilibrium point is established. A numerical example is given to demonstrate the effectiveness of the theoretical results.

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Periodical:

Applied Mechanics and Materials (Volumes 58-60)

Pages:

1136-1141

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.58-60.1136

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Online since:

June 2011

Authors:

Hong Wen Xu

Keywords:

Brouwer Degree, Cohen-Grossberg Model, Equilibrium, Inverse Hö Lder Functions, Neural Network (NN), Stability

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References

[1] M. Cohen and S. Grossberg , Absolute stability and global pattern formation and parallel storage by competitive neural networks. IEEE Trans. Syst. Man and Cyb, Vol. 13(1983), 815-826.

DOI: 10.1109/tsmc.1983.6313075

Google Scholar

[2] S. Grossberg, Nonlinear neural networks principles, mechanisms, and architectures. Neural Networks, Vol. 1(1988), 17-66.

DOI: 10.1016/0893-6080(88)90021-4

Google Scholar

[3] J. Cao and X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Phys. D., Vol. 212(2005), 54-65.

DOI: 10.1016/j.physd.2005.09.005

Google Scholar

[4] Y. Chen, Global asymptotic stability of delayed Cohen-Grossberg neural networks. IEEE Trans. Circuits Syst.I., Vol. 53(2006), 351-357.

DOI: 10.1109/tcsi.2005.856047

Google Scholar

[5] C. Huang, Dynamics of a class of Cohen-Grossberg neural networks with time-varying delays. Non-linear Anal.: Real WorldAppl., Vol. 8(2007), 40-52.

DOI: 10.1016/j.nonrwa.2005.04.008

Google Scholar

[6] H. Wu, Global exponential stability of Hoped neural networks with delays and inverse Lipschitz neuron activations. Nonlinear Anal.: Real World Appl., Vol. 10(2009), 2297-2306.

DOI: 10.1016/j.nonrwa.2008.04.016

Google Scholar

[7] H. Wu and X. Xue, Stability analysis for neural networks with inverse Lipschizan neuron activations and impulses. Appl. Math. Model., Vol. 32(2008), 2347-2359.

DOI: 10.1016/j.apm.2007.09.002

Google Scholar

[8] K. Deimling: Nonlinear Functional Analysis, Springer-Verlag, Berlin. (1985).

Google Scholar

[9] P.K. Miller and A.N. Michel: Differential Equations, New York: Academic. (1982).

Google Scholar