忆阻突触耦合环形Hopfield神经网络动力学分析及其电路实现

doi:10.19596/j.cnki.1001-246x.8338

摘要/Abstract

摘要：

提出一种新型忆阻器模型, 利用标准非线性理论分析三个忆阻特性, 并设计模拟电路。基于忆阻突触, 构建一个忆阻突触耦合环形Hopfield神经网络模型。采用分岔图、李雅普诺夫指数谱、时序图等方法, 揭示与忆阻突触密切相关的特殊动力学行为。数值仿真表明: 在忆阻突触权重的影响下, 它能够产生多种对称簇发放电模式和复杂的混沌行为。实现了该忆阻环形神经网络的模拟等效电路, 并由PSIM电路仿真验证MATLAB数值仿真的正确性。

关键词: 忆阻器, Hopfield神经网络, 簇发放电, 共存吸引子, 模拟电路

Abstract:

A new memristor model is proposed and three memristive characteristics are analyzed with standard nonlinear theory.Analog circuit of the memristor is designed.Then, a memristor synapse-coupled ring Hopfield neural network is constructed based on the memristor synapse.Special dynamical behaviors closely related to the memristor synapse are revealed by adopting bifurcation diagrams, Lyapunov exponents, time series, etc.It shows that the memristive neural network generates multiple symmetrical bursting firing patterns and complex chaotic behavior at different memristive synaptic weight.Finally, an equivalent analog circuit of the memristive neural network is designed, and correctness of MATLAB numerical simulation is verified with PSIM circuit simulations.

Key words: memristor, Hopfield neural network, bursting firing, coexisting attractors, analog circuit

罗佳, 孙亮, 乔印虎. 忆阻突触耦合环形Hopfield神经网络动力学分析及其电路实现[J]. 计算物理, 2022, 39(1): 109-117.

Jia LUO, Liang SUN, Yinhu QIAO. Dynamical Analysis and Circuit Implementation of a Memristor Synapse-coupled Ring Hopfield Neural Network[J]. Chinese Journal of Computational Physics, 2022, 39(1): 109-117.

图/表 12

图1 输入信号幅度/频率相关的v-i曲线(a) F=0.2, 不同幅度下的紧磁滞回线；(b) A=2, 不同频率下的紧磁滞回线

Fig.1 v-i curves at different input signal amplitude/frequency (a) pinched hysteresis loops at different amplitudes (F=0.2); (b) pinched hysteresis loops at different frequencies (A=2)

图2 广义忆阻器电路

Fig.2 Circuit of a general memristor

图3 局部有源忆阻器电路PSIM仿真结果(a) f=2 kHz, 不同电压幅度下的紧磁滞回线; (b) H=2 V, 不同电压频率下的紧磁滞回线

Fig.3 PSIM simulation results of a locally active memristor circuit (a) pinched hysteresis loops at different voltage amplitudes (f=2 kHz); (b) pinched hysteresis loops at different voltage frequencies (H=2 V)

图4 忆阻突触耦合环形神经网络结构

Fig.4 The structure of a memristor synapse-coupled loop neural network

图5 忆阻参数α的动力学状态分布(a) 分岔图; (b) 李雅普诺夫指数谱

Fig.5 Dynamical states related to memristor parameter α (a) bifurcation diagram; (b) Lyapunov exponents

图6 忆阻突触权重参数α取不同值时系统动力学的时序图和相位图(a) 周期簇发放电(α=1)；(b) 混沌簇发放电(α=10)；(c)混沌放电(α=18)；(d) 周期吸引子(α=1)；(e) 混沌吸引子(α=10)；(f) 混沌吸引子(α=18)；(g) 周期簇发放电(α=30)；(h) 周期簇发放电(α=40)；(i) 周期尖峰放电(α=48)；(j)周期吸引子(α=30)；(k)周期吸引子(α=40)；(l)周期吸引子(α=48)

Fig.6 Time sequences and phase plots in dynamical system under different memristive synaptic weight parameter α (a) periodic bursting firing (α=1); (b) chaotic bursting firing (α=10); (c) chaos firing (α=18); (d) period attractor (α=1); (e) chaos attractor (α=10); (f) chaos attractor (α=18); (g) periodic bursting firing (α=30); (h) periodic bursting firing (α=40); (i) periodic spiking firing (α=48); (j) period attractor (α=30); (k) period attractor (α=40); (l) period attractor (α=48)

图7 不同初始条件下的共存簇发行为(a) 对称周期簇发放电(α=1)；(b) 对称混沌簇发放电(α=10)；(c) 对称周期尖峰放电(α=48)

Fig.7 Coexisting bursting behaviors under different initial conditions (a) symmetrical periodic bursting firing (α=1); (b) symmetrical chaotic bursting firing (α=10); (c) symmetrical periodic spiking firing (α=48)

图8 关于忆阻突触权重参数β动力学状态分布(a) 分岔图; (b) 李雅普诺夫指数谱

Fig.8 Dynamical states related to memristive synaptic weight parameter β (a) bifurcation diagram; (b) Lyapunov exponents

图9 忆阻突触权重参数β取不同值时系统所产生的吸引子相图(a) 混沌吸引子(β=0.3); (b) 对称准周期吸引子(β=0.5); (c) 对称周期吸引子(β=0.6)

Fig.9 Phase plots of attractor in system with different memristive synaptic weight parameter β (a) chaos attractor (β=0.3); (b) symmetrical quasi-period attractor (β=0.5); (c) symmetrical period attractor (β=0.6)

图10 忆阻突触耦合环形Hopfield神经网络电路

Fig.10 Circuit of memristor synapse-coupled loop Hopfield neural network

图11 忆阻突触耦合环形Hopfield神经网络电路仿真结果(a) 周期簇发放电RL1=50 kΩ (α=1); (b) 对称混沌簇发放电RL1=5 kΩ (α=10); (c) 混沌放电RL1=2.8 kΩ (α=18); (d) 对称周期簇发放电RL1=1.25 kΩ (α=40)

Fig.11 Simulation results of memristor synapse-coupled loop Hopfield neural network circuit (a) periodic bursting firng with RL1=50 kΩ (α=1); (b) symmetrical chaotic bursting firing with RL1=5 kΩ (α=10); (c) chaos firing with RL1=2.8 kΩ (α=18); (d) symmetrical periodic bursting firing with RL1=1.25 kΩ (α=40)

图12 忆阻突触耦合环形Hopfield神经网络电路仿真结果(a) 混沌吸引子RL2=166.67 kΩ (β=0.3); (b) 对称准周期吸引子RL2=100 kΩ (β=0.5); (c) 对称周期吸引子RL2=83.33 kΩ (β=0.6)

Fig.12 Simulation results of memristor synapse-coupled loop Hopfield neural network circuit (a) chaos attractor with RL2=166.67 kΩ (β=0.3); (b) symmetrical quasi-period attractor with RL2=100 kΩ (β=0.5); (c) symmetrical period attractor with RL2=83.33 kΩ (β=0.6)

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