Almost Periodic Functions on the Quantum Time Scale and Applications

• Main Author: Yongkun Li
• Format: Article
• Language: English
• Published: Hindawi Limited 2019-01-01
• Series: Discrete Dynamics in Nature and Society
• Online Access: http://dx.doi.org/10.1155/2019/4529159

In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study the existence and uniqueness of almost periodic solutions of dynamic equations on the quantum time scale by Lyapunov method. Then, we give an equivalent definition of almost periodic functions on the quantum time scale. Finally, as an application, we propose a class of high-order Hopfield neural networks on the quantum time scale and establish the existence and global exponential stability of almost periodic solutions of this class of neural networks.