Anti-periodic behavior for quaternion-valued delayed cellular neural networks

Zhenhua Duan,Changjin Xu

doi:10.1186/s13662-021-03327-7

Abstract

In this manuscript, quaternion-valued delayed cellular neural networks are studied. Applying the continuation theorem of coincidence degree theory, inequality techniques and a Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of anti-periodic solutions for quaternion-valued delayed cellular neural networks is presented. The obtained results supplement some earlier publications that deal with the anti-periodic solutions of quaternion-valued neural networks with distributed delay or impulse or state-dependent delay or inertial term. Computer simulations are displayed to check the derived analytical results.

Highlights

It is well known that cellular neural networks have widely been applied in many areas such as optimization, associative memories, image processing, psychophysics, and adaptive pattern recognition [1,2,3]
Wang et al [7] investigated the global stability of periodic solution of cellular neural networks; Li and Wang [8] studied the almost periodic solutions of delayed cellular neural networks; Aouiti et al [9] analyzed the exponential stability of piecewise pseudo almost periodic solution for neutral-type neural networks; Li and Xiang [10] dealt with the antiperiodic solution of Cohen–Grossberg neural networks; Wang [11] handled the finitetime synchronization of fuzzy delayed cellular neural networks
Remark 4.2 In [29, 37, 46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67], the authors dealt with stability of delayed neural networks or other delayed models, but all the scholars in [29, 37, 46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67] did not investigate the stability of anti-periodic solution of quaternion-valued neural networks (QVNNs)

Summary

Introduction

It is well known that cellular neural networks have widely been applied in many areas such as optimization, associative memories, image processing, psychophysics, and adaptive pattern recognition [1,2,3]. Some research results on anti-periodic solution of neural networks have been available. In order to make up for this deficiency, in the present manuscript, we will consider the anti-periodic solution of a class of quaternion-valued cellular neural networks (QVCNNs).

Results

Conclusion