Abstract
In this paper, global exponential stability of Cohen-Grossberg neural networks with reaction-diffusion and Dirichlet boundary conditions is considered by using an approach based on the delay differential inequality and the fixed-point theorem. Some sufficient conditions are obtained to guarantee that the reaction-diffusion Cohen-Grossberg neural networks are globally exponentially stable. The results presented in this paper are the improvement and extension of the existed ones in some existing works.
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References
Grossberg, S.: Nonlinear Difference-differential Equations in Prediction and Learning Theory. In: Proceedings of the National Academy of Sciences, vol. 58, pp. 1329–1334 (1967)
Cohen, M.A., Grossberg, S.: Absolute Stability of Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics, SMC 13, 815–826 (1983)
Hopfield, J.J.: Neurons with Graded Response Have Collective Computational Pproperties like Those of Two-state Neurons. Proc. Natl. Academy Sci. 81, 3088–3092 (1984)
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circuits. Syst. 35, 1257–1272 (1988)
Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circ. Syst. I 42, 354–366 (1995)
Yi, Z., Heng, A., Leung, K.S.: Convergence Analysis of Cellular Neural Networks with Unbounded Delay. IEEE Trans. Circuits Syst. I 48, 680–687 (2001)
Yuan, K., Cao, J.D., Li, H.X.: Robust Stability of Switched Cohen-Grossberg Neural Networks with Mixed Time-varying Delays. IEEE Transactions on Systems Man and Cybernetics B-Cybernetics 36, 1356–1363 (2006)
Yang, Z.C., Xu, D.Y.: Impulsive Effects on Stability of Cohen-Grossberg Neural Networks with Variable Delays. Applied Mathematics and Computation 177, 63–78 (2006)
Wang, Z.D., Liu, Y.R., Li, M.Z., Liu, X.H.: Stability Analysis for Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays. IEEE Transactions on Neural Networks 17, 814–820 (2006)
Liao, X.F., Li, C.D.: Global Attractivity of Cohen-Grossberg Model with Finite and Infinite Delays. Journal of Mathematical Analysis and Applications 315, 244–262 (2006)
Cao, J.D., Li, X.L.: Stability in Delayed Cohen-Grossberg Neural Networks: LMI Optimization Approach. Physica D-Nonlinear Phenomena 212, 54–65 (2005)
Chen, T.P., Rong, L.B.: Robust Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-delays. IEEE Transactions on Neural Networks 15, 203–206 (2004)
Song, Q.K., Cao, J.D.: Global Exponential Stability and Existence of Periodic Solutions in BAM Networks with Delays and Reaction Diffusion Terms. Chaos, Solitons & Fractals 23, 421–430 (2005)
Song, Q.K., Cao, J.D., Zhao, Z.J.: Periodic Solutions and Its Exponential Stability of Reaction-Diffusion Recurrent Neural Networks with Continuously Distributed Delays. Nonlinear Analysis: Real World Applications 7, 65–80 (2006)
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Fu, C., Zhu, C. (2007). Global Exponential Stability of Cohen-Grossberg Neural Networks with Reaction-Diffusion and Dirichlet Boundary Conditions. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_7
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DOI: https://doi.org/10.1007/978-3-540-74205-0_7
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