Nonnegative periodicity on high-order proportional delayed cellular neural networks involving $ D $ operator

Xiaojin Guo; Chuangxia Huang; Jinde Cao; Xiaojin Guo; Chuangxia Huang; Jinde Cao

doi:10.3934/math.2021135

AIMS Mathematics

2021, Volume 6, Issue 3: 2228-2243. doi: 10.3934/math.2021135

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Research article

Nonnegative periodicity on high-order proportional delayed cellular neural networks involving $ D $ operator

1.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China
2.
School of Mathematics, Southeast University, Nanjing 211189, China
3.
Yonsei Frontier Lab, Yonsei University, Seoul 03722, Korea

Received: 28 September 2020 Accepted: 03 December 2020 Published: 11 December 2020
MSC : 34C25, 34K13, 34K25

This paper aims to deal with the dynamic behaviors of nonnegative periodic solutions for one kind of high-order proportional delayed cellular neural networks involving $ D $ operator. By utilizing Lyapunov functional approach, combined with some dynamic inequalities, we establish a new assertion to guarantee the existence and global exponential stability of nonnegative periodic solutions for the addressed networks. The obtained results supplement and improve some existing ones. In addition, the correctness of the analytical results are verified by numerical simulations.
- high-order cellular neural network,
- proportional delay,
- nonnegative periodic solution,
- global exponential stability,
- D operator
Citation: Xiaojin Guo, Chuangxia Huang, Jinde Cao. Nonnegative periodicity on high-order proportional delayed cellular neural networks involving $ D $ operator[J]. AIMS Mathematics, 2021, 6(3): 2228-2243. doi: 10.3934/math.2021135

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Abstract

This paper aims to deal with the dynamic behaviors of nonnegative periodic solutions for one kind of high-order proportional delayed cellular neural networks involving $ D $ operator. By utilizing Lyapunov functional approach, combined with some dynamic inequalities, we establish a new assertion to guarantee the existence and global exponential stability of nonnegative periodic solutions for the addressed networks. The obtained results supplement and improve some existing ones. In addition, the correctness of the analytical results are verified by numerical simulations.

References

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