Predefined-time and finite-time synchronization control of fuzzy Cohen-Grossberg neural networks with two additive time-varying delay

Teng Dong; Minghui Jiang; Teng Dong; Minghui Jiang

doi:10.3934/math.2026016

AIMS Mathematics

2026, Volume 11, Issue 1: 366-398. doi: 10.3934/math.2026016

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Research article

Predefined-time and finite-time synchronization control of fuzzy Cohen-Grossberg neural networks with two additive time-varying delay

Teng Dong ¹,
Minghui Jiang ^{2
,
,}

1.
College of Mathematical and Physics, China Three Gorges University, Yichang, Hubei, 443002, China
2.
College of Science, China Three Gorges University, Yichang, Hubei, 443000, China

Received: 10 October 2025 Revised: 27 November 2025 Accepted: 08 December 2025 Published: 05 January 2026
MSC : 93D21, 93D40

This paper investigated novel predefined-time stability theorems for time-delayed fuzzy Cohen-Grossberg neural networks. A novel predefined-time stability lemma was introduced via a newly developed inequality-based analytical framework.The theoretical results demonstrated that, compared to existing stability criteria in the literature, is provided more precise estimation of settling time boundaries, but also effectively reduced conservatism. To validate the effectiveness of the proposed lemma, the stability theorem was applied to the synchronization control problem of fuzzy Cohen-Grossberg neural networks (FCGNNs).To address this, an adaptive control strategy was proposed, employing a discontinuous state-feedback approach for the response neural network. Rigorous algebraic criteria was established to ensure synchronization within the specified time frame, in line with prior discussions. The effectiveness of the proposed synchronization method was empirically verified through numerical case studies.
- predefined-time synchronization,
- fixed-time synchronization,
- fuzzy Cohen-Grossberg neural networks,
- additive time-varying delay
Citation: Teng Dong, Minghui Jiang. Predefined-time and finite-time synchronization control of fuzzy Cohen-Grossberg neural networks with two additive time-varying delay[J]. AIMS Mathematics, 2026, 11(1): 366-398. doi: 10.3934/math.2026016

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Abstract

This paper investigated novel predefined-time stability theorems for time-delayed fuzzy Cohen-Grossberg neural networks. A novel predefined-time stability lemma was introduced via a newly developed inequality-based analytical framework.The theoretical results demonstrated that, compared to existing stability criteria in the literature, is provided more precise estimation of settling time boundaries, but also effectively reduced conservatism. To validate the effectiveness of the proposed lemma, the stability theorem was applied to the synchronization control problem of fuzzy Cohen-Grossberg neural networks (FCGNNs).To address this, an adaptive control strategy was proposed, employing a discontinuous state-feedback approach for the response neural network. Rigorous algebraic criteria was established to ensure synchronization within the specified time frame, in line with prior discussions. The effectiveness of the proposed synchronization method was empirically verified through numerical case studies.

References

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