Tbilisi Mathematical Journal

Almost automorphic solutions for neutral type CNNs with time-varying delays and $D$ operator on time scales

Abstract

In this paper, we propose a new concept of almost automorphic functions on a new type of almost periodic time scales. Based on inequality analysis techniques on time scales, the exponential dichotomy of linear dynamic equations on time scales and the Banach's fixed point theorem, we establish the existence and global exponential stability of almost automorphic solutions for a class of neutral type cellular neural networks with time-varying delays and $D$ operator on time scales. We give a numerical example to illustrate the feasibility of our results.

Note

This work is supported by the National Natural Sciences Foundation of People's Republic of China under Grant 11361072.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 2 (2019), 89-100.

Dates
Received: 1 December 2018
Accepted: 20 March 2019
First available in Project Euclid: 21 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1561082570

Digital Object Identifier
doi:10.32513/tbilisi/1561082570

Mathematical Reviews number (MathSciNet)
MR3973262

Citation

Li, Bing; Li, Yongkun. Almost automorphic solutions for neutral type CNNs with time-varying delays and $D$ operator on time scales. Tbilisi Math. J. 12 (2019), no. 2, 89--100. doi:10.32513/tbilisi/1561082570. https://projecteuclid.org/euclid.tbilisi/1561082570

References

• G. M. N'Guérékata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic Plenum, New York-Boston-Moscow-London, 2001.
• L. Zhao, Y. Li, B. Li, Weighted pseudo-almost automorphic solutions of high-order Hopfield neural networks with neutral distributed delays, Neural Comput. Appl. 29(7) (2018) 513-527.
• Y. K. Li, L. Yang, Almost automorphic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales, Appl. Math. Comput. 242 (2014) 679-693.
• A. Murat, H. C. Koyuncuoglu, Y. N. Raffoul, Almost automorphic solutions of delayed neutral dynamic systems on hybrid domains, Appl. Anal. 10 (2016) 128-151.
• L. Yao, Global convergence of CNNs with neutral type delays and $D$ operator, Neural Comput. Applic. 29(1) (2018) 105-109.
• A. Zhang, Pseudo almost periodic solutions for neutral type SICNNs with D operator, J. Exp. Theor. Artif. Intell. 29(4) (2017) 795-807.
• H. M. Srivastava, K. L. Tseng, S. J. Tseng, J. C. Lo, Some weighted Opial-type inequalities on time scales, Taiwanese J. Math. 14 (2010) 107-122.
• H. M. Srivastava, K. L. Tseng, S. J. Tseng, J. C. Lo, Some generalizations of Maroni's inequality on time scales, Math. Inequal. Appl. 14 (2011) 469-480.
• Y. K. Li, C. Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal. 2011 (2011), Article ID 341520, 22pp.
• C. Wang, Y. K. Li, Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales, Ann. Polon. Math. 108 (2013) 225-240.
• C. Lizama, J. G. Mesquita, Almost automorphic solutions of dynamic equations on time scales, J. Funct. Anal. 265 (2013) 2267-2311.
• Y. K. Li, B. Li, Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scales, SpringerPlus 2016; 5(1): 1096.
• Y. K. Li, P. Wang, Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales, Discrete Contin. Dyn. Syst. Ser. S 10 (2017) 463-473.
• Y. K. Li, C. Wang, Almost periodic functions on time scales and applications, Discrete Dyn. Nat. Soc. 2011 (2011), Article ID 727068, 20 pages.