Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method

Ruoyu Wei; Jinde Cao; Wenhua Qian; Changfeng Xue; Xiaoshuai Ding; Ruoyu Wei; Jinde Cao; Wenhua Qian; Changfeng Xue; Xiaoshuai Ding

doi:10.3934/math.2021405

AIMS Mathematics

2021, Volume 6, Issue 7: 6915-6932. doi: 10.3934/math.2021405

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Research article

Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method

1.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
School of Mathematics, Southeast University, Nanjing 210096, China
3.
Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
4.
The Computer Science and Engineering Department, Yunnan University, Qunming 210096, China
5.
School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng 224051, China
6.
School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an, China

Received: 28 January 2021 Accepted: 15 April 2021 Published: 22 April 2021
MSC : 00A69

In this paper, we focus on the finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks. To cope with the effect caused by inertial (second-order) term, most of the previous literature use the variable translation to reduce the order. Different from that, by directly designing a Lyapunov functional and feedback controller, a novel non-reduced order method is proposed in this paper to solve the finite-time (fixed-time) stabilization problem of inertial memristive Cohen-Grossberg neural networks. Two kinds of time delays are considered in our network model, novel criteria are then derived for both cases. Lastly, numerical examples are given to verify the validity of the theoretical results.
- Cohen-Grossberg neural networks,
- inertial term,
- mixed time delays,
- finite-time (fixed-time) stabilization
Citation: Ruoyu Wei, Jinde Cao, Wenhua Qian, Changfeng Xue, Xiaoshuai Ding. Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method[J]. AIMS Mathematics, 2021, 6(7): 6915-6932. doi: 10.3934/math.2021405

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Abstract

In this paper, we focus on the finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks. To cope with the effect caused by inertial (second-order) term, most of the previous literature use the variable translation to reduce the order. Different from that, by directly designing a Lyapunov functional and feedback controller, a novel non-reduced order method is proposed in this paper to solve the finite-time (fixed-time) stabilization problem of inertial memristive Cohen-Grossberg neural networks. Two kinds of time delays are considered in our network model, novel criteria are then derived for both cases. Lastly, numerical examples are given to verify the validity of the theoretical results.

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