https://doi.org/10.1140/epjs/s11734-025-01721-w
Regular Article
Analysis of chimera states in memristive autapse Morris–Lecar neuronal networks and circuit design
1
School of Electronic and Information Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, China
2
School of Mechanical and Electrical Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, China
3
School of Design and Art, Lanzhou University of Technology, 730050, Lanzhou, China
Received:
21
February
2025
Accepted:
29
May
2025
Published online:
15
July
2025
In this paper, based on the local active memristive autapse Morris–Lecar neuron model, a multi-layer neural network model consisting of a central node and a multi-layer ring network is established. Different neuron nodes in the network are coupled by electrical synapses. The two-parameter bifurcation diagram is used to describe the rich discharge modes of the ring star network under the influence of system parameters and non-system parameters, respectively. Memristive autapse gain can also cause the transition of the system discharge mode. An adaptive coherence measurement method is used to quantitatively analyze the coherence degree of the neurons in the network. The interlayer synchronization error is used to quantitatively analyze the synchronization between different layers of the neural network. Then, the coupling strength of the center node and the interlayer coupling strength were changed to analyze the transition process of the chimera state of the ring-star neuronal network, and the transient chimera phenomenon was found. It is also found that the coupling strength of the center node can promote the synchronization behavior between the first layer neurons, and a sufficiently large interlayer coupling strength will spread the influence of the central node on the first layer network to the rest layer network. When the coupling strength of the center node is large enough, enhancing the coupling strength between layers can promote the complete synchronization of the neural network. Finally, a ring-star neuronal network circuit composed of 13 neurons is built and the correctness of the numerical simulation results is verified by circuit simulation analysis.
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© The Author(s), under exclusive licence to EDP Sciences, 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.
