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Field and delay effects on synchronization in a multilayer memristive neuronal network with a hub

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  • Tian, Huaigu
  • Wang, Zhen
  • Cao, Zelin
  • Sun, Bai

Abstract

This study investigates synchronization dynamics in a three-layer network of memristive Hindmarsh–Rose (m-HR) neurons with a central hub node. The outer layers consist of globally coupled identical m-HR neurons, while the middle layer contains a single hub neuron that relays signals between the outer layers through time-delayed inter-layer connections. Two types of inter-layer coupling are considered: delayed electrical synapses, which act through the spike voltage, and delayed field couplings, modeled via memristive interactions involving the flux variable. By analyzing intra- and inter-layer synchronization errors across varying coupling strengths and time delays, we explore how these factors influence synchronization performance. Our results reveal that increasing time delay generally deteriorates synchronization, with the degradation pattern depending on the coupling type. In the case of electrical synapses, synchronization loss is irregular with increasing delay, while under field coupling, the synchronization threshold rises systematically. Notably, stronger intra-layer coupling significantly mitigates the adverse effects of time delay, preserving intra-layer synchronization even at high delay values. These findings highlight the importance of coupling configuration and local connectivity strength in maintaining coherent dynamics in multilayer neuronal networks subject to transmission delays.

Suggested Citation

  • Tian, Huaigu & Wang, Zhen & Cao, Zelin & Sun, Bai, 2025. "Field and delay effects on synchronization in a multilayer memristive neuronal network with a hub," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925013050
    DOI: 10.1016/j.chaos.2025.117292
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    References listed on IDEAS

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    1. Lixia Ye & Yonghui Xia & Jin-liang Yan & Haidong Liu, 2020. "Synchronization Analysis for Stochastic Inertial Memristor-Based Neural Networks with Linear Coupling," Complexity, Hindawi, vol. 2020, pages 1-14, July.
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    3. Sriram, Sridevi & Rajagopal, Karthikeyan & Karthikeyan, Anitha & Akgul, Akif, 2023. "Memristive field effect in a single and multilayer neural network with different connection topologies," Applied Mathematics and Computation, Elsevier, vol. 457(C).
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