物理学报2026，Vol.75Issue(17)：10-24,15.DOI:10.7498/aps.75.20260520
一种基于离散二阶忆阻器的KTz神经元模型:动力学分析与硬件实现
A KTz neuron model based on a discrete second-order memristor:dynamical analysis and hardware implementation
摘要
Abstract
Compared with first-order memristors,second-order memristors exhibit better bio-inspired characteristics due to their possession of two internal state variables and can describe more complex nonlinear modulation effects.Motivated by this advantage,this work proposes a KTz neuron model based on a discrete second-order memristor.By introducing a discrete second-order memristor with dual internal state variables into the KTz neuron,the proposed model achieves a unified description of the autaptic feedback mechanism and the external electromagnetic modulation effect,thus enhancing its capability to characterize complex neuronal firing behaviors.The firing dynamics of the model are systematically investigated by means of equilibrium-point analysis,Lyapunov exponent spectra,bifurcation diagrams,phase portraits,and time-series analysis.The experimental results show that the proposed model can generate abundant firing patterns,including periodic firing,quasiperiodic firing,chaotic bursting firing,and hyperchaotic firing,and can also exhibit rich nonlinear dynamical phenomena such as state transition and coexisting attractors.These results also indicate that the model is highly sensitive to parameters and initial conditions,as well as complex nonstationary dynamical characteristics.To further evaluate the complexity of the proposed system,spectral entropy is introduced to measure the irregularity and complexity of the generated sequences from the frequency-domain perspective.Meanwhile,the statistical randomness of the output sequences is verified by the NIST SP 800-22 test suite.The experimental results demonstrate that the chaotic sequences generated by the proposed model possess good complexity and satisfactory statistical randomness.Finally,a digital hardware implementation platform based on the STM32F407 microcontroller is constructed to realize real-time iterative computation and signal output of the model.The experimental results obtained from the hardware platform are in good agreement with the numerical simulations,which verifies the feasibility of the proposed model.These results suggest that the model has potential application value in complex neuronal dynamical modeling,chaotic sequence generation,and related engineering implementations.关键词
离散二阶忆阻器/离散神经元/放电模式/硬件实现Key words
discrete second-order memristor/discrete neuron/firing pattern/hardware implementation引用本文复制引用
王梦蛟,廖雨舟..一种基于离散二阶忆阻器的KTz神经元模型:动力学分析与硬件实现[J].物理学报,2026,75(17):10-24,15.基金项目
湖南省自然科学基金(批准号:2025JJ50391)、湖南省教育厅科学研究基金(批准号:24A0124)和国家自然科学基金(批准号:62071411)资助的课题. Project supported by the Natural Science Foundation of Hunan Province,China(Grant No.2025JJ50391),the Research Foundation of Education Department of Hunan Province,China(Grant No.24A0124),and the National Natural Science Foundation of China(Grant No.62071411). （批准号:2025JJ50391）
