https://doi.org/10.1140/epjp/s13360-025-07013-5
Regular Article
Modeling and synchronization research of adaptive networks
1
School of Automation and Electrical Engineering, Lanzhou University of Technology, 730050, Lanzhou, China
2
Department of Physics, Lanzhou University of Technology, 730050, Lanzhou, China
a
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Received:
19
August
2025
Accepted:
29
October
2025
Published online:
9
November
2025
Abstract
In recent years, adaptive neural networks have received significant attention due to their wide application in brain-like computing, pattern recognition, and information processing. However, most current research still focuses on the mathematical modeling and theoretical analysis level, and the research on their physical implementation at the device level is still relatively limited. To address this issue, this paper proposes a device implementation idea for adaptive neural networks based on memristors, and the FitzHugh–Nagumo (FHN) neuron is used for measuring local kinetics of the network. This work directly introduces the real response behavior of memristors and studies their influence on the network synchronization process. Memristors in the model not only play the role of chemical synapses but also introduce device constraint characteristics by constructing a σ matrix, which characterizes the influence of device constraints on the network synchronization behavior. Comparative analysis shows that after introducing the real device characteristics, the system synchronization behavior shows some differences compared to the ideal model; although the synchronization threshold changes slightly, the overall synchronization performance remains nearly the same, demonstrating the important influence of physical non-ideality on network behavior. Using the master stability function (MSF) theory to solve the system synchronization conditions, this paper further reveals the coupling mechanism between device characteristics and network dynamics. By changing the connection density (ki) and introducing an external electric field, the enhancement effect of network structure and external driving on synchronization performance was explored. In addition, to achieve active control of network firing synchronization, this paper designed an adaptive coupling strength regulation strategy based on node energy difference. Numerical simulations show that as the control gain parameter g increases, the system synchronization speed significantly accelerates. In summary, this paper not only proposes a device implementation method for adaptive networks based on memristors, but also reveals the profound influence of device-level non-ideality on the complex network synchronization behavior by introducing a real physical response model, providing theoretical and simulation support for the hardware realization of brain-like intelligent systems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
