Abstract
This paper is devoted to investigation of the existence of the equilibrium point and its globally exponential stability for reaction-diffusion Cohen-Grossberg neural networks with variable coefficients and distributed delays by means of the homotopic mapping theory and Lyapunov-functional method. The sufficient conditions obtained which are easily verifiable, have a wider adaptive range. Finally, a numerical example verifies the theoretical analysis.
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
Xu, Z., Qiao, H., Peng, J., Zhang, B.: A Comparative Study of Two Modeling Approaches in Neural Networks. J. Neural Networks 17, 73–85 (2004)
Cao, J.: An Estimation of the Domain of Attraction and Convergence Rate for Hopfield Continuous Feedback Neural Networks. Phys. Lett. A 325, 370–374 (2004)
Cao, J., Liang, L.: Boundedness and Stability for Cohen-Grossberg Neural Network with Time-varying Delays. J. Math. Anal. Appl. 296, 665–685 (2004)
Cao, J., Wang, J.: Globally Exponentially Stability and Periodicity of Recurrent Neural Networks with Time Delays. IEEE Trans. Circuits Syst. I 52, 920–931 (2005)
Zhang, J., Suda, Y., Komine, H.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Variable Delays. Phys. Lett. A 338, 44–50 (2005)
Hasting, A.: Global Stability in Lotka-Volterra Systems with Diffusion. J. Math. Biol. 6, 163–168 (1978)
Liang, J., Cao, J.: Global Exponential Stability of Reaction-Diffusion Recurrent Neural Networks with Time-varying Delays. Phys. Lett. A 314, 434–442 (2003)
Liao, X., Li, C.: Stability in Gilpin-Ayala Competition Models with Diffusion. Nonlinear Anal. TMA. 18, 1751–1758 (1997)
Liao, X., Li, C., Wong, K.: Criteria for Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 17, 1401–1414 (2004)
Rothe, F.: Convergence to the Equilibrium State in the Volterra-Lotka Diffusion Equations. J. Math. Biol. 3, 319–324 (1976)
Song, Q., Cao, J.: 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., Zhao, Z., Li, Y.: Global Exponential Stability of BAM Neural Networks with Distributed Delays and Reaction-diffusion Terms. Phys. Lett. A 335, 213–225 (2005)
Wang, L., Xu, D.: Global Exponential Stability of Reaction-diffusion Hopfield Neural Networks with Variable Delays. Sci. China Ser. E 33, 488–495 (2003)
Xiong, W., Cao, J.: Global Exponential Stability of Discrete-time Cohen-Grossberg Neural Networks. Neurocomputing 64, 433–446 (2005)
Yuan, K., Cao, J.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Multiple Time-varying Delays. LNCS, vol. 73, pp. 78–83 (2004)
Zhang, J., Suda, Y., Komine, H.: GlobalExponential Stability of Cohen-Grossberg Neural Networks with Variable Delays. Phys. Lett. A 338, 44–50 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kao, Y., Bao, S. (2009). Exponential Stability of Reaction-Diffusion Cohen-Grossberg Neural Networks with S-Type Distributed Delays. In: Wang, H., Shen, Y., Huang, T., Zeng, Z. (eds) The Sixth International Symposium on Neural Networks (ISNN 2009). Advances in Intelligent and Soft Computing, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01216-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-01216-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01215-0
Online ISBN: 978-3-642-01216-7
eBook Packages: EngineeringEngineering (R0)