Synchronization dynamics in fractional-order FitzHugh–Nagumo neural networks with time-delayed coupling

Canhong Long; Zuozhi Liu; Can Ma; Canhong Long; Zuozhi Liu; Can Ma

doi:10.3934/math.2025397

AIMS Mathematics

2025, Volume 10, Issue 4: 8673-8687. doi: 10.3934/math.2025397

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Synchronization dynamics in fractional-order FitzHugh–Nagumo neural networks with time-delayed coupling

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, China
2.
School of Mathematics, Northwest University, Xi'an, 710069, China

Received: 22 January 2025 Revised: 02 April 2025 Accepted: 03 April 2025 Published: 15 April 2025
MSC : 26A33, 34K37

Studying the synchronization of neural networks is crucial for understanding brain function and diagnosing neurological disorders. However, most existing research focuses on integer-order systems and overlooks the effects of time-delay coupling. To address this, this paper was devoted to investigating the synchronization behaviors of time-delay coupled fractional-order FitzHugh–Nagumo networks. The sufficient conditions for the synchronization of two coupled neurons were derived using the Lyapunov stability criterion. Furthermore, the synchronization factor was utilized to elucidate the combined effects of coupling strength and time delay, as well as the influence of time delay on fractional-order dynamics. The analysis began with two coupled systems, and the results were then extended to networks with a larger number of nodes. Numerical examples were presented to illustrate the obtained results.
- fractional-order,
- neuronal models,
- FithzHugh–Nagumo neuronal network,
- time-delayed coupling,
- synchronization
Citation: Canhong Long, Zuozhi Liu, Can Ma. Synchronization dynamics in fractional-order FitzHugh–Nagumo neural networks with time-delayed coupling[J]. AIMS Mathematics, 2025, 10(4): 8673-8687. doi: 10.3934/math.2025397

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Abstract

Studying the synchronization of neural networks is crucial for understanding brain function and diagnosing neurological disorders. However, most existing research focuses on integer-order systems and overlooks the effects of time-delay coupling. To address this, this paper was devoted to investigating the synchronization behaviors of time-delay coupled fractional-order FitzHugh–Nagumo networks. The sufficient conditions for the synchronization of two coupled neurons were derived using the Lyapunov stability criterion. Furthermore, the synchronization factor was utilized to elucidate the combined effects of coupling strength and time delay, as well as the influence of time delay on fractional-order dynamics. The analysis began with two coupled systems, and the results were then extended to networks with a larger number of nodes. Numerical examples were presented to illustrate the obtained results.

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