Tbilisi Mathematical Journal

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

Bing Li and Yongkun Li

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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

Subjects
Primary: 34K40: Neutral equations
Secondary: 34K20: Stability theory 92B20: Neural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx]

Keywords
cellular neural networks almost automorphic solution $D$ operator time scales

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


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