Finite-time stability analysis of fractional-order Cohen–Grossberg neural networks with time-varying delays and fuzzy logics

Qijun Dong; Liguang Wan; Ailong Wu; Tao Li; Qijun Dong; Liguang Wan; Ailong Wu; Tao Li

doi:10.3934/math.2026928

AIMS Mathematics

2026, Volume 11, Issue 7: 23016-23049. doi: 10.3934/math.2026928

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Research article

Finite-time stability analysis of fractional-order Cohen–Grossberg neural networks with time-varying delays and fuzzy logics

1.
School of Electrical Engineering and Automation, Hubei Normal University, Huangshi 435002, China
2.
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 03 June 2026 Revised: 07 July 2026 Accepted: 15 July 2026 Published: 29 July 2026
MSC : 34A08, 93D40

This paper addresses the finite-time stability problem for a class of fractional-order Cohen–Grossberg neural networks characterized by fuzzy logic operators and time-varying delays. The coexistence of variable delays and fuzzy feedback structures poses considerable challenges in deriving effective stability conditions. To tackle these difficulties, a delay-dependent estimation strategy based on a weighted envelope framework is developed to characterize the influence of delayed states. Subsequently, a novel fractional Gronwall-type inequality is established and utilized to derive a sufficient finite-time stability criterion for the investigated neural network model. The obtained criterion explicitly captures the effects of fuzzy min/max operations and time-varying delays. Finally, three simulation examples are provided to verify the applicability and effectiveness of the proposed theoretical results.
- fractional-order Cohen–Grossberg neural networks,
- fuzzy logics,
- finite-time stability,
- time-varying delays,
- Gronwall-type inequality
Citation: Qijun Dong, Liguang Wan, Ailong Wu, Tao Li. Finite-time stability analysis of fractional-order Cohen–Grossberg neural networks with time-varying delays and fuzzy logics[J]. AIMS Mathematics, 2026, 11(7): 23016-23049. doi: 10.3934/math.2026928

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Abstract

This paper addresses the finite-time stability problem for a class of fractional-order Cohen–Grossberg neural networks characterized by fuzzy logic operators and time-varying delays. The coexistence of variable delays and fuzzy feedback structures poses considerable challenges in deriving effective stability conditions. To tackle these difficulties, a delay-dependent estimation strategy based on a weighted envelope framework is developed to characterize the influence of delayed states. Subsequently, a novel fractional Gronwall-type inequality is established and utilized to derive a sufficient finite-time stability criterion for the investigated neural network model. The obtained criterion explicitly captures the effects of fuzzy min/max operations and time-varying delays. Finally, three simulation examples are provided to verify the applicability and effectiveness of the proposed theoretical results.

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