中国物理B ›› 2026, Vol. 35 ›› Issue (6): 68708-068708.doi: 10.1088/1674-1056/ae3609

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Dynamical behavior analysis for small-world scale-free neural networks

Jieyu Lu(鲁婕妤)1, Jiapeng Ouyang(欧阳佳鹏)1, Xue Zhao(赵雪)2, and Minglin Ma(马铭磷)1,†   

  1. 1 School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;
    2 Xiangtan Central Hospital, Xiangtan 411105, China
  • 收稿日期:2025-11-11 修回日期:2026-01-04 接受日期:2026-01-09 发布日期:2026-06-23
  • 通讯作者: Minglin Ma E-mail:minglin_ma@xtu.edu.cn
  • 基金资助:
    This work was supported by the Key Research and Development Plan of Hunan Province (Grant No. 2026QK3023) and the Natural Science Foundation Project of Hunan Province (Grant Nos. 2026JJ50521 and 2026JJ81304).

Dynamical behavior analysis for small-world scale-free neural networks

Jieyu Lu(鲁婕妤)1, Jiapeng Ouyang(欧阳佳鹏)1, Xue Zhao(赵雪)2, and Minglin Ma(马铭磷)1,†   

  1. 1 School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;
    2 Xiangtan Central Hospital, Xiangtan 411105, China
  • Received:2025-11-11 Revised:2026-01-04 Accepted:2026-01-09 Published:2026-06-23
  • Contact: Minglin Ma E-mail:minglin_ma@xtu.edu.cn
  • Supported by:
    This work was supported by the Key Research and Development Plan of Hunan Province (Grant No. 2026QK3023) and the Natural Science Foundation Project of Hunan Province (Grant Nos. 2026JJ50521 and 2026JJ81304).

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摘要： The neural networks of the human brain exhibit dual structural characteristics of small-world and scale-free networks, and their electrical activity is readily modulated by electromagnetic fields. Constructing neural network models that mimic biological structures is crucial for elucidating the brain's information processing mechanisms and the pathological basis of neurological disorders. This paper constructs a small-world scale-free neural network (SWSFNN) model under electromagnetic effects using discrete memristors. By optimizing network topology via graph theory, we systematically investigate how memristor initial values and electromagnetic induction intensity influence the network dynamics. Numerical simulations reveal that memristor initial values affect neuronal firing patterns and regulate network synchronization. We further find a spontaneous "synchronization-cluster synchronization-synchronization" transition under constant parameters. This finding demonstrates that, even in the absence of parameter variations, the inherent nonlinear interactions within the neural network system can drive spontaneous state transitions, thereby generating rich dynamical behaviors. Furthermore, increasing electromagnetic induction intensity also enhances network synchronization. This study provides a theoretical foundation for understanding the nonlinear dynamical mechanisms and synchronization control of neural networks in electromagnetic environments, offering insights for neural computation and information processing.

关键词: synchronization, electromagnetic effect, small-world characteristics, memristor

Abstract: The neural networks of the human brain exhibit dual structural characteristics of small-world and scale-free networks, and their electrical activity is readily modulated by electromagnetic fields. Constructing neural network models that mimic biological structures is crucial for elucidating the brain's information processing mechanisms and the pathological basis of neurological disorders. This paper constructs a small-world scale-free neural network (SWSFNN) model under electromagnetic effects using discrete memristors. By optimizing network topology via graph theory, we systematically investigate how memristor initial values and electromagnetic induction intensity influence the network dynamics. Numerical simulations reveal that memristor initial values affect neuronal firing patterns and regulate network synchronization. We further find a spontaneous "synchronization-cluster synchronization-synchronization" transition under constant parameters. This finding demonstrates that, even in the absence of parameter variations, the inherent nonlinear interactions within the neural network system can drive spontaneous state transitions, thereby generating rich dynamical behaviors. Furthermore, increasing electromagnetic induction intensity also enhances network synchronization. This study provides a theoretical foundation for understanding the nonlinear dynamical mechanisms and synchronization control of neural networks in electromagnetic environments, offering insights for neural computation and information processing.

Key words: synchronization, electromagnetic effect, small-world characteristics, memristor

中图分类号:  (Neural networks)

  • 87.85.dq
05.45.Xt (Synchronization; coupled oscillators) 87.19.lj (Neuronal network dynamics) 05.45.-a (Nonlinear dynamics and chaos)