Abstract
For the convenience of computer simulation, the discrete-time systems in practice are often considered. In this paper, Discrete-time cellular neural networks (DTCNNs) are formulated and studied in a regime where they act as a switchboard for oscillating inputs. Several sufficient conditions are obtained to ensure DTCNNs with delays have a periodic orbit and this periodic orbit is globally attractive using a method based on the inequality method and the contraction mapping principle. Finally, simulations results are also discussed via one illustrative example.
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
Grassi, G.: On Discrete-time Cellular Neural Networks for Associative Memories. IEEE Trans. Circuits Syst. I. 48, 107–111 (2001)
Liu, D., Michel, A.N.: Sparsely Interconnected Neural Networks for Associative Memories with Applications to Cellular Neural Networks. IEEE Trans. Circ. Syst. II 41, 295–307 (1994)
Michel, A.N., Wang, K., Liu, D., Ye, H.: Qualitative Limitations Incurred in Implementations of Recurrent Neural Networks. IEEE Trans. Contr. Syst. Technol. 15, 52–65 (1995)
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circuits Syst. 35, 1257–1272 (1988)
Liao, X.X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circuits and Systems I. 50, 268–275 (2003)
Huang, D.S.: A Constructive Approach for Finding Arbitrary Roots of Polynomials by Neural Networks. IEEE Trans. Neural Networks 15, 477–491 (2004)
Zeng, Z.G., Wang, J., Liao, X.X.: Global Exponential Stability of A General Class of Recurrent Neural Networks with Time-varying Delays. IEEE Trans. Circuits and Syst. I 50, 1353–1358 (2003)
Zeng, Z.G., Wang, J., Liao, X.X.: Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. Circuits and Syst. I 51, 2313–2324 (2004)
Sun, C., Feng, C.: Exponential Periodicity of Continuous-time and Discrete-time Neural Networks with Delays. Neural Processing Letters 19, 131–146 (2004)
Sun, C., Feng, C.: Exponential Periodicity and Stability of Delayed Neural Networks. Mathematics and Computers in Simulation 66, 469–478 (2004)
Huang, D.S.: The Local Minima Free Condition of Feedforward Neural Networks for Outer-supervised Learning. IEEE Trans. Systems, Man and Cybernetics 28B, 477–480 (1998)
Zeng, Z.G., Huang, D.S., Wang, Z.F.: Stability Analysis of Discrete-time Cellular Neural Networks. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 114–119. Springer, Heidelberg (2004)
Yosida, K.: Functional Analysis. Springer, Berlin (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zeng, Z., Chen, B., Wang, Z. (2005). Globally Attractive Periodic State of Discrete-Time Cellular Neural Networks with Time-Varying Delays. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_44
Download citation
DOI: https://doi.org/10.1007/11427391_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
Online ISBN: 978-3-540-32065-4
eBook Packages: Computer ScienceComputer Science (R0)