Almost automorphic functions on time scales and almost automorphic solutions to shunting inhibitory cellular neural networks on time scales
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Authors
Yongkun Li
- Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China.
Bing Li
- Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China.
Xiaofang Meng
- Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China.
Abstract
In this paper, we first propose a new definition of almost automorphic functions on almost periodic time
scales and study some of their basic properties. Then we prove a result ensuring the existence of an almost
automorphic solution for both the linear nonhomogeneous dynamic equation on time scales and its associated
homogeneous equation, assuming that the latter admits an exponential dichotomy. Finally, as an application
of our results, we establish the existence and global exponential stability of almost automorphic solutions to
a class of shunting inhibitory cellular neural networks with time-varying delays on time scales. Our results
about the shunting inhibitory cellular neural networks with time-varying delays on time scales are new both
for the case of differential equations (the time scale \(\mathbb{T} = \mathbb{R}\)) and difference equations (the time scale \(\mathbb{T} = \mathbb{Z}\)).
Share and Cite
ISRP Style
Yongkun Li, Bing Li, Xiaofang Meng, Almost automorphic functions on time scales and almost automorphic solutions to shunting inhibitory cellular neural networks on time scales, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 1190--1211
AMA Style
Li Yongkun, Li Bing, Meng Xiaofang, Almost automorphic functions on time scales and almost automorphic solutions to shunting inhibitory cellular neural networks on time scales. J. Nonlinear Sci. Appl. (2015); 8(6):1190--1211
Chicago/Turabian Style
Li, Yongkun, Li, Bing, Meng, Xiaofang. "Almost automorphic functions on time scales and almost automorphic solutions to shunting inhibitory cellular neural networks on time scales." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 1190--1211
Keywords
- Time scales
- Almost automorphic functions
- Dynamic equations
- Exponential dichotomy.
MSC
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