Stability analysis of Cohen-Grossberg neural networks with time-varying delay by flexible terminal interpolation method

Biwen Li; Yibo Sun; Biwen Li; Yibo Sun

doi:10.3934/math.2023906

AIMS Mathematics

2023, Volume 8, Issue 8: 17744-17764. doi: 10.3934/math.2023906

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Research article

Stability analysis of Cohen-Grossberg neural networks with time-varying delay by flexible terminal interpolation method

Biwen Li ,
Yibo Sun ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 07 March 2023 Revised: 10 April 2023 Accepted: 08 May 2023 Published: 24 May 2023
MSC : 34H15

In the paper, the existence and uniqueness of the equilibrium point in the Cohen-Grossberg neural network (CGNN) are first studied. Additionally, a switched Cohen-Grossberg neural network (SCGNN) model with time-varying delay is established by introducing a switched system to the CGNN. Based on reducing the conservativeness of the system, a flexible terminal interpolation method is proposed. Using an adjustable parameter to divide the invariant time-delay interval into multiple adjustable terminal interpolation intervals $ (2^{\imath +1}-3) $, more moments when signals are transmitted slowly can be captured. To this end, a new Lyapunov-Krasovskii functional (LKF) is constructed, and the stability of SCGNN can be estimated. Using the LKF method, a quadratic convex inequality, linear matrix inequalities (LMIs) and ordinary differential equation theory, a new form of stability criterion is obtained and specific instances are given to prove the applicability of the new stability criterion.
- switched system,
- Cohen-Grossberg neural networks,
- flexible terminal interpolation method,
- linear matrix inequalities,
- stability analysis
Citation: Biwen Li, Yibo Sun. Stability analysis of Cohen-Grossberg neural networks with time-varying delay by flexible terminal interpolation method[J]. AIMS Mathematics, 2023, 8(8): 17744-17764. doi: 10.3934/math.2023906

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Abstract

In the paper, the existence and uniqueness of the equilibrium point in the Cohen-Grossberg neural network (CGNN) are first studied. Additionally, a switched Cohen-Grossberg neural network (SCGNN) model with time-varying delay is established by introducing a switched system to the CGNN. Based on reducing the conservativeness of the system, a flexible terminal interpolation method is proposed. Using an adjustable parameter to divide the invariant time-delay interval into multiple adjustable terminal interpolation intervals $ (2^{\imath +1}-3) $, more moments when signals are transmitted slowly can be captured. To this end, a new Lyapunov-Krasovskii functional (LKF) is constructed, and the stability of SCGNN can be estimated. Using the LKF method, a quadratic convex inequality, linear matrix inequalities (LMIs) and ordinary differential equation theory, a new form of stability criterion is obtained and specific instances are given to prove the applicability of the new stability criterion.

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