Finite-time stability of equilibrium solutions for the inertial neural networks via the figure analysis method

Huaying Liao; Zhengqiu Zhang; Huaying Liao; Zhengqiu Zhang

doi:10.3934/mbe.2023159

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3379-3395. doi: 10.3934/mbe.2023159

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Finite-time stability of equilibrium solutions for the inertial neural networks via the figure analysis method

Huaying Liao ¹,
Zhengqiu Zhang ^{2
,
,}

1.
School of Mathematics and Information Science, Nanchang Normal University, Nanchang 330032, China
2.
School of Mathematics, Hunan University, Changsha 410082, China

Received: 25 August 2022 Revised: 10 November 2022 Accepted: 22 November 2022 Published: 06 December 2022

The existence and finite-time stability (FTS) of equilibrium point (EP) for a kind of inertial neural networks (INNS) with varying-time delays is studied. Firstly, by adopting the degree theory and the maximum-valued method, a sufficient condition in the existence of EP is attained. Then by adopting the maximum-valued approach and the figure analysis approach, without adopting the matrix measure theory, linear matrix inequality (LMI), and FTS theorems, a sufficient condition in the FTS of EP for the discussed INNS is proposed.
- EP,
- FTS,
- degree theory,
- maximum-valued way,
- INNS,
- figure analysis way
Citation: Huaying Liao, Zhengqiu Zhang. Finite-time stability of equilibrium solutions for the inertial neural networks via the figure analysis method[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3379-3395. doi: 10.3934/mbe.2023159

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Abstract

The existence and finite-time stability (FTS) of equilibrium point (EP) for a kind of inertial neural networks (INNS) with varying-time delays is studied. Firstly, by adopting the degree theory and the maximum-valued method, a sufficient condition in the existence of EP is attained. Then by adopting the maximum-valued approach and the figure analysis approach, without adopting the matrix measure theory, linear matrix inequality (LMI), and FTS theorems, a sufficient condition in the FTS of EP for the discussed INNS is proposed.

References

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