中国物理B ›› 2026, Vol. 35 ›› Issue (6): 60501-060501.doi: 10.1088/1674-1056/ae5f06

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Chaotic bursting and burst synchronization in a discrete dual-Rulkov neural network with memristive synaptic coupling

Ke Meng(孟珂)1, Yifan Bu(卜一帆)2, Yinghong Cao(曹颖鸿)1,†, Suo Gao(高锁)1, Qi Li(李琦)3,4, Chunpeng Wang(王春鹏)3,4, and Jun Mou(牟俊)1   

  1. 1 School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China;
    2 Zhongshan School of Medicine, Sun Yat-sen University, Guangzhou, Guangdong 510080, China;
    3 Key Laboratory of Computing Power Network and Information Security, Ministry of Education, National Supercomputer Center in Jinan, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China;
    4 Shandong Provincial Key Laboratory of Computer Networks, Shandong Fundamental Research Center for Computer Science, Jinan 250013, China
  • 收稿日期:2026-03-14 修回日期:2026-04-07 接受日期:2026-04-14 发布日期:2026-06-05
  • 通讯作者: Yinghong Cao E-mail:caoyinghong@dlpu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 62541206, 62502250, and 62571079), the Liaoning Provincial Science and Technology Plan Joint Project (Grant No. 2024-MSLH-033), the Liaoning Provincial Department of Education Basic Scientific Research Projects for Higher Education Institutions (Grant Nos. LJ142510152002 and LJ142510152003), and the Dalian Science and Technology Talent Innovation Support Policy Implementation Plan–Young Science and Technology Star (Grant No. 2025RQ32).

Chaotic bursting and burst synchronization in a discrete dual-Rulkov neural network with memristive synaptic coupling

Ke Meng(孟珂)1, Yifan Bu(卜一帆)2, Yinghong Cao(曹颖鸿)1,†, Suo Gao(高锁)1, Qi Li(李琦)3,4, Chunpeng Wang(王春鹏)3,4, and Jun Mou(牟俊)1   

  1. 1 School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China;
    2 Zhongshan School of Medicine, Sun Yat-sen University, Guangzhou, Guangdong 510080, China;
    3 Key Laboratory of Computing Power Network and Information Security, Ministry of Education, National Supercomputer Center in Jinan, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China;
    4 Shandong Provincial Key Laboratory of Computer Networks, Shandong Fundamental Research Center for Computer Science, Jinan 250013, China
  • Received:2026-03-14 Revised:2026-04-07 Accepted:2026-04-14 Published:2026-06-05
  • Contact: Yinghong Cao E-mail:caoyinghong@dlpu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 62541206, 62502250, and 62571079), the Liaoning Provincial Science and Technology Plan Joint Project (Grant No. 2024-MSLH-033), the Liaoning Provincial Department of Education Basic Scientific Research Projects for Higher Education Institutions (Grant Nos. LJ142510152002 and LJ142510152003), and the Dalian Science and Technology Talent Innovation Support Policy Implementation Plan–Young Science and Technology Star (Grant No. 2025RQ32).

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摘要： A discrete dual-Rulkov neural network with memristive synaptic coupling is constructed to investigate chaotic bursting dynamics and burst synchronization. First, a memristive synapse model suitable for discrete-time neurons is established, and its pinched hysteresis loop (PHL) fingerprint and local activity are verified. Based on this synapse model, a five-dimensional memristively coupled discrete neural system is formulated. By combining Lyapunov exponent spectra (LEs), bifurcation analysis, and equilibrium stability analysis, chaotic and hyperchaotic bursting behaviors induced by variations in the coupling gain are revealed, together with their dynamical evolution characteristics. Furthermore, to characterize irregular spiking activities during chaotic bursting, a joint framework based on the phase-locking value (PLV) and burst envelope correlation (EnvCorr) is introduced, through which three bursting regimes, namely, in-phase bursting (IPB), phaseshifted bursting (PSB), and desynchronized bursting (DB), are identified. Finally, a digital signal processor (DSP)-based real-time hardware implementation is carried out, and the good qualitative agreement between experimental and numerical results demonstrates the physical feasibility of the proposed model.

关键词: memristor, Rulkov neuron, chaotic bursting, burst synchronization, DSP implementation

Abstract: A discrete dual-Rulkov neural network with memristive synaptic coupling is constructed to investigate chaotic bursting dynamics and burst synchronization. First, a memristive synapse model suitable for discrete-time neurons is established, and its pinched hysteresis loop (PHL) fingerprint and local activity are verified. Based on this synapse model, a five-dimensional memristively coupled discrete neural system is formulated. By combining Lyapunov exponent spectra (LEs), bifurcation analysis, and equilibrium stability analysis, chaotic and hyperchaotic bursting behaviors induced by variations in the coupling gain are revealed, together with their dynamical evolution characteristics. Furthermore, to characterize irregular spiking activities during chaotic bursting, a joint framework based on the phase-locking value (PLV) and burst envelope correlation (EnvCorr) is introduced, through which three bursting regimes, namely, in-phase bursting (IPB), phaseshifted bursting (PSB), and desynchronized bursting (DB), are identified. Finally, a digital signal processor (DSP)-based real-time hardware implementation is carried out, and the good qualitative agreement between experimental and numerical results demonstrates the physical feasibility of the proposed model.

Key words: memristor, Rulkov neuron, chaotic bursting, burst synchronization, DSP implementation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Xt (Synchronization; coupled oscillators) 87.19.lj (Neuronal network dynamics) 87.19.lg (Synapses: chemical and electrical (gap junctions))