Fixed-time synchronization of memristive neural networks with time-varying delays via a new stability criterion

Junfeng Tong; Minghui Jiang; Junfeng Tong; Minghui Jiang

doi:10.3934/math.2026314

AIMS Mathematics

2026, Volume 11, Issue 3: 7633-7658. doi: 10.3934/math.2026314

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Fixed-time synchronization of memristive neural networks with time-varying delays via a new stability criterion

Junfeng Tong ¹,
Minghui Jiang ^{2
,
,}

1.
College of Mathematics and Physics, China Three Gorges University, Yichang 443002, Hubei, China
2.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, Hubei, China

Received: 10 February 2026 Revised: 11 March 2026 Accepted: 17 March 2026 Published: 23 March 2026
MSC : 34K20, 93D05, 93C10

This paper investigates the fixed-time synchronization problem of memristive neural networks with time-varying delays by proposing a novel fixed-time stability theorem. Compared with existing results such as Lemmas 2.3 and 2.4, the proposed theorem provides a tighter upper bound estimate of the settling time, making the calculated convergence time closer to the actual evolution process of the system. Furthermore, the theorem removes the parameter constraints inherent in Lemma 2.5, thereby offering broader applicability. Based on the derived criteria, the influence of power function coefficients on the actual convergence rate is explored in detail. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results.
- differential equations,
- time-varying delay,
- memristor,
- neural networks,
- fixed-time synchronization
Citation: Junfeng Tong, Minghui Jiang. Fixed-time synchronization of memristive neural networks with time-varying delays via a new stability criterion[J]. AIMS Mathematics, 2026, 11(3): 7633-7658. doi: 10.3934/math.2026314

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Abstract

This paper investigates the fixed-time synchronization problem of memristive neural networks with time-varying delays by proposing a novel fixed-time stability theorem. Compared with existing results such as Lemmas 2.3 and 2.4, the proposed theorem provides a tighter upper bound estimate of the settling time, making the calculated convergence time closer to the actual evolution process of the system. Furthermore, the theorem removes the parameter constraints inherent in Lemma 2.5, thereby offering broader applicability. Based on the derived criteria, the influence of power function coefficients on the actual convergence rate is explored in detail. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results.

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