Huang, Tingwen Exponential stability of delayed fuzzy cellular neural networks with diffusion. (English) Zbl 1138.35414 Chaos Solitons Fractals 31, No. 3, 658-664 (2007). Summary: The exponential stability of delayed fuzzy cellular neural networks (FCNN) with diffusion is investigated. Exponential stability, significant for applications of neural networks, is obtained under conditions that are easily verified by a new approach. Earlier results on the exponential stability of FCNN with time-dependent delay, which is a special case of the model studied in this paper, are improved without using the time-varying term condition d\(\tau (t)/\)d\(t < \mu \). Cited in 42 Documents MSC: 35R10 Partial functional-differential equations 35B35 Stability in context of PDEs 68U10 Computing methodologies for image processing 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory Keywords:fuzzy cellular neural networks; diffusion effect; exponential stability PDFBibTeX XMLCite \textit{T. Huang}, Chaos Solitons Fractals 31, No. 3, 658--664 (2007; Zbl 1138.35414) Full Text: DOI References: [1] Cao, J.; Wang, J., Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Trans Circ Syst I, 50, 34-44 (2003) · Zbl 1368.34084 [2] Hastings, A., Global stability in Lotka-Volterra systems with diffusion, J Math Biol, 6, 163-168 (1978) · Zbl 0393.92013 [3] Horn, R. A.; Johnson, C. R., Matrix analysis (1990), Cambridge University Press: Cambridge University Press London · Zbl 0704.15002 [4] Liang, J.; Cao, J., Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays, Phys Lett A, 314, 434-442 (2003) · Zbl 1052.82023 [5] Liao, X. X.; Jia, L., Stability in Gilpin-Ayala competition models with diffusion, Nonlinear Anal, 28, 1751-1758 (1997) · Zbl 0872.35054 [6] Liu, Y.; Tang, W., Exponential stability of fuzzy cellular neural networks with constant time-varying delays, Phys Lett A, 323, 224-233 (2004) · Zbl 1118.81400 [7] Yang, T.; Yang, L. B.; Wu, C. W.; Chua, L. O., Fuzzy cellular neural networks: theory, Proc IEEE Int Workshop Cellular Neural Networks Appl, 181-186 (1996) [8] Yang, T.; Yang, L. B., The global stability of fuzzy cellular neural network, Circ Syst I: Fundam Theory Appl, 43, 880-883 (1996) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.