Weyl almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks with time-varying delays

Yongkun Li; Xiaoli Huang; Xiaohui Wang; Yongkun Li; Xiaoli Huang; Xiaohui Wang

doi:10.3934/math.2022271

AIMS Mathematics

2022, Volume 7, Issue 4: 4861-4886. doi: 10.3934/math.2022271

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Research article

Weyl almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks with time-varying delays

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received: 08 November 2021 Revised: 13 December 2021 Accepted: 17 December 2021 Published: 28 December 2021
MSC : 34K14, 34K20, 92B20

We consider the existence and stability of Weyl almost periodic solutions for a class of quaternion-valued shunting inhibitory cellular neural networks with time-varying delays. In order to overcome the incompleteness of the space composed of Weyl almost periodic functions, we first obtain the existence of a bounded continuous solution of the system under consideration by using the fixed point theorem, and then prove that the bounded solution is Weyl almost periodic by using a variant of Gronwall inequality. Then we study the global exponential stability of the Weyl almost periodic solution by using the inequality technique. Even when the system we consider degenerates into a real-valued one, our results are new. A numerical example is given to illustrate the feasibility of our results.
- quaternion-valued neural network,
- Weyl almost periodic solution,
- global exponential stability,
- time-varying delays
Citation: Yongkun Li, Xiaoli Huang, Xiaohui Wang. Weyl almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks with time-varying delays[J]. AIMS Mathematics, 2022, 7(4): 4861-4886. doi: 10.3934/math.2022271

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Abstract

We consider the existence and stability of Weyl almost periodic solutions for a class of quaternion-valued shunting inhibitory cellular neural networks with time-varying delays. In order to overcome the incompleteness of the space composed of Weyl almost periodic functions, we first obtain the existence of a bounded continuous solution of the system under consideration by using the fixed point theorem, and then prove that the bounded solution is Weyl almost periodic by using a variant of Gronwall inequality. Then we study the global exponential stability of the Weyl almost periodic solution by using the inequality technique. Even when the system we consider degenerates into a real-valued one, our results are new. A numerical example is given to illustrate the feasibility of our results.

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