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<p>As synaptic devices, memristors can effectively emulate the connectivity and information transmission between biological neurons. However, many existing memristive neuron models remain limited in their ability to generate rich dynamical complexity. To address this, we propose a novel one-dimensional Rulkov neuron model. By coupling two such neurons through a sine-function-based memristor acting as a synapse, we construct a three-dimensional discrete memristive Rulkov neuron map (DMRN) capable of exhibiting high complexity. Numerical simulations reveal that the proposed map exhibits diverse dynamical behaviors, including periodicity, quasi-periodicity, chaos, and hyperchaos, as well as both heterogeneous and homogeneous multistability. Furthermore, complexity analysis indicates that the map maintains high dynamical complexity across various parameter planes, outperforming many existing memristive neuron models. Finally, a DSP-based hardware circuit was implemented to capture various types of attractors generated by the DMRN, validating the scientific soundness and practical feasibility of the proposed model.</p>

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Discrete memristor neuron model with multistability and its application

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Mingjie Zhou,
  • Guodong Li,
  • Hepeng Pan

摘要

As synaptic devices, memristors can effectively emulate the connectivity and information transmission between biological neurons. However, many existing memristive neuron models remain limited in their ability to generate rich dynamical complexity. To address this, we propose a novel one-dimensional Rulkov neuron model. By coupling two such neurons through a sine-function-based memristor acting as a synapse, we construct a three-dimensional discrete memristive Rulkov neuron map (DMRN) capable of exhibiting high complexity. Numerical simulations reveal that the proposed map exhibits diverse dynamical behaviors, including periodicity, quasi-periodicity, chaos, and hyperchaos, as well as both heterogeneous and homogeneous multistability. Furthermore, complexity analysis indicates that the map maintains high dynamical complexity across various parameter planes, outperforming many existing memristive neuron models. Finally, a DSP-based hardware circuit was implemented to capture various types of attractors generated by the DMRN, validating the scientific soundness and practical feasibility of the proposed model.