Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales
-
1769
Downloads
-
2823
Views
Authors
Bing Li
- School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, Yunnan 650500, People's Republic of China.
Yongkun Li
- Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China.
Abstract
In this paper, we consider a class of neutral type fuzzy cellular neural networks with time-varying delays and \(D\) operator on time scales. Based on inequality analysis techniques on time scales and a fixed point theorem and the theory of calculus on time scales, we obtain the existence and global exponential stability of anti-periodic solutions for this class of the networks. Finally, a numerical example is given to illustrate the feasibility of our results.
Share and Cite
ISRP Style
Bing Li, Yongkun Li, Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 6119--6131
AMA Style
Li Bing, Li Yongkun, Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales. J. Nonlinear Sci. Appl. (2017); 10(11):6119--6131
Chicago/Turabian Style
Li, Bing, Li, Yongkun. "Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 6119--6131
Keywords
- Fuzzy cellular neural networks
- anti-periodic solution
- \(D\) operator
- global exponential stability
- time scales
MSC
References
-
[1]
P. Balasubramaniam, V. Vembarasan, Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses, Comput. Math. Appl., 62 (2011), 1838–1861.
-
[2]
H.-M. Bao, Existence and exponential stability of periodic solution for BAM fuzzy Cohen-Grossberg neural networks with mixed delays , Neural Proc. Lett., 43 (2016), 871–885.
-
[3]
M. Bohner, A. Peterson , Dynamic equations on time scales , An introduction with applications. Birkhuser Birkhäuser Boston, Inc., Boston, MA (2001)
-
[4]
L. O. Chua, L. Yang , Cellular neural networks: applications, IEEE Trans. Circuits and Systems, 35 (1988), 1273–1290.
-
[5]
L. O. Chua, L. Yang, Celluar neural networks: theory, IEEE Trans. Circuits and Systems, 35 (1988), 1257–1272.
-
[6]
Z.-D. Huang , Almost periodic solutions for fuzzy cellular neural networks with time-varying delays, Neural Comput. Appl., 28 (2017), 2313–2320.
-
[7]
R.-W. Jia, , Fuzzy Sets and Systems, 319 (2017), 70–80.
-
[8]
Y.-K. Li, X.-R. Chen, L. Zhao, Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales, Neurocomputing, 72 (2009), 1621–1630.
-
[9]
Y.-K. Li, C. Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal., 2011 (2011), 22 pages.
-
[10]
Y.-K. Li, C. Wang, Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses, Fuzzy Sets and Systems, 217 (2013), 62–79.
-
[11]
Y.-K. Li, L. Yang, W.-Q. Wu , Periodic solutions for a class of fuzzy BAM neural networks with distributed delays and variable coefficients, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 20 (2010), 1551–1565.
-
[12]
Y.-K. Li, T.-W. Zhang, Global exponential stability of fuzzy interval delayed neural networks with impulses on time scales, Int. J. Neural Syst., 19 (2009), 449–456.
-
[13]
B.-W. Liu, Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Anal. Real World Appl., 14 (2013), 559–566.
-
[14]
Y. Luo, W.-B. Wang, J.-H. Shen, Existence of positive periodic solutions for two kinds of neutral functional differential equations, Appl. Math. Lett., 21 (2008), 581–587.
-
[15]
C.-J. Xu, Q.-M. Zhang, Y.-S. Wu, Existence and exponential stability of periodic solution to fuzzy cellular neural networks with distributed delays, Int. J. Fuzzy Syst., 18 (2016), 41–51.
-
[16]
T. Yang, L.-B. Yang , The global stability of fuzzy cellular neural network, IEEE Trans. Circuits Systems I Fund. Theory Appl., 43 (1996), 880–883.
-
[17]
T. Yang, L.-B. Yang, C.-W. Wu, L. O. Chua, Fuzzy cellular neural networks: applications, Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings, Seville, Spain, CNNA-96 (1996), 225–230.
-
[18]
T. Yang, L.-B. Yang, C.-W. Wu, L. O. Chua, Fuzzy cellular neural networks: theory, Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings, Seville, Spain, CNNA-96 (1996), 181– 186.
-
[19]
K. Yuan, J.-D. Cao, J.-M. Deng , Exponential stability and periodic solutions of fuzzy cellular neural networks with timevarying delays, Neurocomputing, 69 (2006), 1619–1627.
-
[20]
Q.-H. Zhang, R.-G. Xiang, Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Phys. Lett. A, 372 (2008), 3971–3977.
-
[21]
L.-L. Zhao, Y.-K. Li, Existence and exponential stability of anti-periodic solutions of high-order Hopfield neural networks with delays on time scales, Differ. Equ. Dyn. Syst., 19 (2011), 13–26.
-
[22]
L.-Q. Zhou, Global asymptotic stability of cellular neural networks with proportional delays, Nonlinear Dynam., 77 (2014), 41–47.
-
[23]
L.-Q. Zhou, X.-B. Chen, Y.-X. Yang, Asymptotic stability of cellular neural networks with multiple proportional delays, Appl. Math. Comput., 229 (2014), 457–466.