On the Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks

A set of criteria is presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals, introducing many parameters and combining with the elementary inequality technique. These criteria have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, earlier results are extended and improved; other results are contained. Two examples are given to illustrate the theory.

[1]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[2]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[3]  Leon O. Chua,et al.  Cellular neural networks with non-linear and delay-type template elements and non-uniform grids , 1992, Int. J. Circuit Theory Appl..

[4]  Leon O. Chua,et al.  Stability of cellular neural networks with dominant nonlinear and delay-type templates. (Memo UCB/ERL No. M92/121.) , 1993 .

[5]  Kiyotoshi Matsuoka,et al.  Stability conditions for nonlinear continuous neural networks with asymmetric connection weights , 1992, Neural Networks.

[6]  Leon O. Chua,et al.  Stability and dynamics of delay-type general and cellular neural networks , 1992 .

[7]  L. Pandolfi,et al.  On stability of cellular neural networks with delay , 1993 .

[8]  Marco Gilli,et al.  Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions , 1994 .

[9]  H Lu,et al.  Unconditioned Stability of Cellular Neural Networks with Delay. , 1997 .

[10]  Jinde Cao,et al.  Stability analysis of delayed cellular neural networks , 1998, Neural Networks.

[11]  Cao Jin-de,et al.  The stability in neural networks with interneuronal transmission delays , 1998 .

[12]  Cao Jinde,et al.  Stability of a class of neural network models with delay , 1999 .

[13]  Jinde Cao.  Stability in cellular neural networks with delays , 1999 .

[14]  Jinde Cao,et al.  On stability of delayed cellular neural networks , 1999 .

[15]  J. Cao.  Global stability analysis in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  J. Cao,et al.  Global stability in delayed cellular neural networks , 1999, Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468).

[17]  Jinde Cao,et al.  Periodic solutions and exponential stability in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Jinde Cao,et al.  On exponential stability and periodic solutions of CNNs with delays , 2000 .

[19]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

[20]  Jinde Cao.  Periodic oscillation and exponential stability of delayed CNNs , 2000 .

[21]  Stability of a Class of Neural Network Models with Delays , 2000 .

[22]  Jinde Cao,et al.  Global Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks , 2000, J. Comput. Syst. Sci..