New Results on Exponential Convergence for Cellular Neural Networks with Continuously Distributed Leakage Delays
This paper discusses the issue of a class of cellular neural networks with continuously distributed delays in the leakage terms. By applying Lyapunov functional method and differential inequality techniques, without assuming the boundedness conditions on the activation functions, a new delay dependent sufficient condition is derived to ensure that all solutions of the networks converge exponentially to the zero point, which corrects some recent results of Xiong and Meng (Electron J Qual Theory Differ Equ, (10):1–12, 2013. http://www.math.u-szeged.hu/ejqtde/).
KeywordsCellular neural network Exponential convergence Continuously distributed delay Leakage term
Mathematics Subject Classification34C25 34K13 34K25
The author would like to express the sincere appreciation to the editor and reviewer for their helpful comments in improving the presentation and quality of the paper. In particular, the author expresses the sincere gratitude to Prof. Bingwen Liu for the helpful discussion when this revision work is carried out.
- 2.Kosok B (1992) Neural networks and fuzzy systems. Prentice-Hall, New DelhiGoogle Scholar
- 8.Yu Y, Jiao W, New results on exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Process Lett doi: 10.1007/s11063-013-9296-7
- 9.Xiong W, Meng J (2013) Exponential convergence for cellular neural networks with continuously distributed delays in the leakage terms, Electron. J Qual Theory Differ Equ (10)1–12; http://www.math.u-szeged.hu/ejqtde/
- 10.Hino Y, Murakami S, Nai T (1991) Functional differential equations with infinite delay. Lecture in Mathematics, 1473. Springer, BerlinGoogle Scholar
- 13.Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements In: Proceedings of 1990 IEEE international workshop on cellular neural networks and their applications, pp 12–25Google Scholar
- 14.Huang L, Li X (2007) Dynamics cellular neural networks. Science Press, Beijing [In Chinese]Google Scholar
- 15.Jia R, Yang M, Convergence for HRNNs with unbounded activation functions and time-varying delays in the leakage terms. Neural Process Lett doi: 10.1007/s11063-013-9290-0
- 16.Xu Y (2012) Anti-periodic solutions for HCNNs with time-varying delays in the leakage terms. Neural Comput Appl. doi: 10.1007/s00521-012-1330-6
- 17.Zhao C, Wang Z (2014) Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Process Lett. doi: 10.1007/s11063-014-9341-1