Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term

ABSTRACT

In this paper, we propose a class of quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term. In order to overcome the difficulty of the non-commutativity of quaternion multiplication, we first decompose the system under consideration into four real-valued systems. Then by using the exponential dichotomy theory of linear differential equations and Banach's fixed point theorem, we establish sufficient conditions to ensure the existence and global exponential stability of almost periodic solutions for this class of neural networks. Finally, a numerical example is given to demonstrate the effectiveness of the obtained result.

KEYWORDS:

• Almost periodic solutions
• quaternion
• shunting inhibitory cellular neural networks
• neutral type
• leakage delays
• exponential stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Sciences Foundation of People's Republic of China [grant number 11361072] and the Science Research Fund of Education Department of Yunnan Province of China [grant number 2017YJS111.]