Almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks with time-varying and distributed delays

作者：Li, Yongkun^*; Wang, Huimei; Meng, Xiaofang

来源：IMA Journal of Mathematical Control and Information, 2019, 36(3): 983-1013.

DOI：10.1093/imamci/dny015

• almost automorphic synchronization
• quaternion-valued neural network
• time delay

In this paper, we consider the problem of the almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying and distributed delays. Firstly, to avoid the non-commutativity of quaternion multiplication, we decompose QVHHNNs into an equivalent real-valued system. Secondly, we use the Banach fixed point theorem to obtain the existence of almost automorphic solutions of QVHHNNs. Thirdly, by designing a novel state-feedback controller and constructing suitable Lyapunov functions, we obtain that the drive-response structure of QVHHNNs with almost automorphic coefficients can realize the exponential synchronization. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.

• 出版日期2019-9
• 单位昆明学院; 云南大学