The measure pseudo almost-periodicty and automorphy in HOHNNs with time-varying delays

Abstract

In this work, we prove some existence, global exponential stability and uniqueness results for measure pseudo almost periodic and automorphic solutions to a class of high-order Hopfield neural networks with delays. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle. Finally, three numerical examples are given to illustrate the effectiveness of our results.

Keywords:

• Pseudo almost periodic solution
• pseudo almost automorphic solution
• measure theory
• high-order Hopfield neural networks
• global exponential stability

AMS Subject Classifications:

• 34K14
• 34K30
• 35B15
• 35K57
• 44A35
• 47D06

Acknowledgments

The authors would like to express their thanks to the editor and anonymous referees for his/her suggestions and comments that improved the quality of the paper.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.