中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10504-010504.doi: 10.1088/1674-1056/ae1728

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Dynamics analysis and DSP implementation of the Rulkov neuron model with memristive synaptic crosstalk

Yichen Bi(毕毅晨)1, Jun Mou(牟俊)1, Herbert Ho-Ching Iu2, Nanrun Zhou(周南润)3, Santo Banerjee4, and Suo Gao(高锁)1,†   

  1. 1 School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China;
    2 School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth 6009, Australia;
    3 School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;
    4 Department of Mathematical Sciences, Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy
  • 收稿日期:2025-08-12 修回日期:2025-10-22 接受日期:2025-10-24 发布日期:2025-12-29
  • 通讯作者: Suo Gao E-mail:gaosuo@dlpu.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (Grant No. 62571079), the Technological Innovation Projects in the Field of Artificial Intelligence in Liaoning Province (Grant No. 2023JH26/10300011), the Basic Scientific Research Projects in the Department of Education of Liaoning Province (Grant No. LJ212410152049), and the Liaoning Provincial Science and Technology Plan Joint Project (Grant No. 2025-BSLH-041).

Dynamics analysis and DSP implementation of the Rulkov neuron model with memristive synaptic crosstalk

Yichen Bi(毕毅晨)1, Jun Mou(牟俊)1, Herbert Ho-Ching Iu2, Nanrun Zhou(周南润)3, Santo Banerjee4, and Suo Gao(高锁)1,†   

  1. 1 School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China;
    2 School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth 6009, Australia;
    3 School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;
    4 Department of Mathematical Sciences, Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy
  • Received:2025-08-12 Revised:2025-10-22 Accepted:2025-10-24 Published:2025-12-29
  • Contact: Suo Gao E-mail:gaosuo@dlpu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Grant No. 62571079), the Technological Innovation Projects in the Field of Artificial Intelligence in Liaoning Province (Grant No. 2023JH26/10300011), the Basic Scientific Research Projects in the Department of Education of Liaoning Province (Grant No. LJ212410152049), and the Liaoning Provincial Science and Technology Plan Joint Project (Grant No. 2025-BSLH-041).

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摘要： The human brain is a complex intelligent system composed of tens of billions of neurons interconnected through synapses, and its intricate network structure has consistently attracted numerous scientists to explore the mysteries of brain functions. However, most existing studies have only verified the biological mimicry characteristics of memristors at the single neuron-synapse level, and there is still a lack of research on memristors simulating synaptic coupling between neurons in multi-neuron networks. Based on this, this paper uses discrete memristors to couple dual discrete Rulkov neurons, and adds synaptic crosstalk between the two discrete memristors to form a neuronal network. A memristor-coupled dual-neuron map, called the Rulkov-memristor-Rulkov (R-M-R) map, is constructed to simulate synaptic connections between neurons in biological tissues. Then, the equilibrium points of the R-M-R map are studied. Subsequently, the effect of parameter variations on the dynamic performance of the R-M-R map is comprehensively analyzed using bifurcation diagram, phase diagram, Lyapunov exponent spectrum (LEs), firing diagram, and spectral entropy (SE) complexity algorithms. In the R-M-R map, diverse categories of periodic, chaotic, and hyperchaotic attractors, as well as different states of firing patterns, can be observed. Additionally, different types of state transitions and coexisting attractors are discovered. Finally, the feasibility of the model in digital circuits is verified using a DSP hardware platform. In this study, the coupling principle of biological neurons is simulated, the chaotic dynamic behavior of the R-M-R map is analyzed, and a foundation is laid for deciphering the complex working mechanisms of the brain.

关键词: Rulkov neuron, discrete memristor, firing patterns, synaptic crosstalk, DSP implementation

Abstract: The human brain is a complex intelligent system composed of tens of billions of neurons interconnected through synapses, and its intricate network structure has consistently attracted numerous scientists to explore the mysteries of brain functions. However, most existing studies have only verified the biological mimicry characteristics of memristors at the single neuron-synapse level, and there is still a lack of research on memristors simulating synaptic coupling between neurons in multi-neuron networks. Based on this, this paper uses discrete memristors to couple dual discrete Rulkov neurons, and adds synaptic crosstalk between the two discrete memristors to form a neuronal network. A memristor-coupled dual-neuron map, called the Rulkov-memristor-Rulkov (R-M-R) map, is constructed to simulate synaptic connections between neurons in biological tissues. Then, the equilibrium points of the R-M-R map are studied. Subsequently, the effect of parameter variations on the dynamic performance of the R-M-R map is comprehensively analyzed using bifurcation diagram, phase diagram, Lyapunov exponent spectrum (LEs), firing diagram, and spectral entropy (SE) complexity algorithms. In the R-M-R map, diverse categories of periodic, chaotic, and hyperchaotic attractors, as well as different states of firing patterns, can be observed. Additionally, different types of state transitions and coexisting attractors are discovered. Finally, the feasibility of the model in digital circuits is verified using a DSP hardware platform. In this study, the coupling principle of biological neurons is simulated, the chaotic dynamic behavior of the R-M-R map is analyzed, and a foundation is laid for deciphering the complex working mechanisms of the brain.

Key words: Rulkov neuron, discrete memristor, firing patterns, synaptic crosstalk, DSP implementation

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Jn (High-dimensional chaos)