Positive stability analysis of pseudo almost periodic solutions for HDCNNs accompanying $ D $ operator

Lilun Zhang; Le Li; Chuangxia Huang

doi:10.3934/dcdss.2021160

Article Contents

2022, Volume 15, Issue 7: 1651-1667. Doi: 10.3934/dcdss.2021160

This issue Previous Article Data-driven control of hydraulic servo actuator based on adaptive dynamic programming Next Article A novel bond stress-slip model for 3-D printed concretes

Positive stability analysis of pseudo almost periodic solutions for HDCNNs accompanying $ D $ operator

1.
College of Meteorology and Oceanography, National University of Defense Technology, Changsha, Hunan 410073, China
2.
School of Mathematics and Statistics, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China

^*Corresponding author: Chuangxia Huang
^*Corresponding author: Chuangxia Huang

Received: August 2021

Revised: September 2021

Early access: December 2021

Published: July 2022

This research was supported by the National Natural Science Foundation of China (Nos. 11971076, 11801562) and the Natural Science Foundation of Hunan Province (No. 2019JJ40142).

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Abstract

In this study, the stable dynamics of a kind of high-order cellular neural networks accompanying $ D $ operators and mixed delays are analyzed. The global existence of bounded positive solutions is substantiated by applying some novel differential inequality analyses. Meanwhile, by exploiting Lyapunov function method, some sufficient criteria are gained to validate the positiveness and globally exponential stability of pseudo almost periodic solutions on the addressed networks. In addition, computer simulations are produced to test the derived analytical findings.

Keywords:

Stability,
positiveness,
pseudo almost periodic solution,
high-order delayed cellular neural networks,
$ D $ operator.

Mathematics Subject Classification: Primary: 34C25, 34K13, 34K25.

Citation:

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Figure 1. Numerical characteristics for solutions $ x(t) $ of HDCNNs (4.1) incorporating distinct initial values: ($ -0.3\cos 2t $, $ 3+\sin 3t $), ($ 2.3\cos 2t $, $ 2+1.8\sin 3t $), ($ 0.5+\cos 3t $, $ -0.8\sin 2t $)

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