具有隐藏超级多稳定性的磁感应HR神经元及其电路实现

doi:10.19596/j.cnki.1001-246x.8476

摘要/Abstract

摘要：

使用磁控忆阻器描述神经元的膜电位与磁通的耦合, 提出一个磁感应HR神经元模型, 通过分岔图、李雅普诺夫指数谱、时序图以及相位图等动力学分析方法揭示它的复杂动力学行为。研究表明: 这种电磁感应HR神经元模型没有任何平衡点, 但可以产生无限多个形状相同但位置不同的隐藏混沌吸引子, 具有隐藏的超级多稳定性特征。此外, 设计了电磁感应HR神经元的模拟等效电路, PSIM电路仿真验证了数值仿真的正确性。

关键词: HR神经元, 忆阻器, 隐藏吸引子, 超级多稳定性, 神经元电路

Abstract:

With a magnetically controlled memristor to describe the coupling between membrane potential and magnetic flux, a magnetic induction HR neuron model is established. Its complex dynamical behavior is revealed with dynamic analysis methods including bifurcation diagrams, Lyapunov exponent spectrum, time sequences, and phase plots. It shows that the magnetic induction HR neuron has no equilibrium points while it can generate infinite hidden chaotic attractors with same topologies and different positions. Namely, the neuron model has the characteristic of hidden extreme multistability. Moreover, an analog equivalent circuit of the magnetic induction HR neuron is designed. Numerical simulations is verified with PSIM circuit simulations.

Key words: HR neuron, memristor, hidden attractors, extreme multistability, neuron circuit

唐利红, 贺宗梅, 姚延立. 具有隐藏超级多稳定性的磁感应HR神经元及其电路实现[J]. 计算物理, 2022, 39(5): 589-597.

Lihong TANG, Zongmei HE, Yanli YAO. Magnetic Induction HR Neuron with Hidden Extreme Multistability and Its Circuit Implementation[J]. Chinese Journal of Computational Physics, 2022, 39(5): 589-597.

图/表 12

图1 隐藏混沌吸引子相图 (a) x-y相平面; (b) x-φ相平面; (c) y-φ相平面

Fig.1 Phase plots of hidden attractors (a) x-y phase plane; (b) x-φ phase plane; (c) y-φ phase plane

图2 李雅普诺夫指数随时间变化

Fig.2 Lyapunov exponents as functions of time

图3 磁感应强度参数k1动力学状态分布(a)分岔图; (b) 李雅普诺夫指数谱

Fig.3 Dynamical distribution related to magnetic induction intensity k1(a) Bifrucation; (b) Lyapunov exponents

图4 不同磁感应强度k1所对应的的吸引子相图(a) 周期1吸引子k1=-3.5; (b) 周期2吸引子k1=-3; (c) 混沌吸引子k1=-2.4; (d) 准周期吸引子k1=-1.8

Fig.4 Phase plots of attractors corresponding to different magnetic induction intensity k1(a) Period-1 attractor at k1=-3.5; (b) Period-2 attractor at k1=-3; (c) Chaotic attractor at k1=-2.4; (d) Quasi-period attractor at k1=-1.8

图5 与初值φ(0)相关的分岔图

Fig.5 Bifrucation diagram related to initial value φ(0)

图6 与初值φ(0)相关的混沌吸引子

Fig.6 Chaotic attractors related to initial value φ(0)

图7 与初值相关的周期吸引子，从左至右，φ(0) = -18π，-16π，-14π，-12π，-10π，-8π，-6π，-4π，-2π，0

Fig.7 Periodic attractors related to initial value, from left to right, φ(0) = -18π, -16π, -14π, -12π, -10π, -8π, -6π, -4π, -2π, 0

图8 磁感应HR神经元电路(a) 余弦忆阻器模拟等效电路; (b) 磁感应HR神经元模拟等效电路

Fig.8 Magnetic induction HR neuron circuit (a) Analog equivalent circuit of cosin memristor; (b) Analog equivalent circuit of magnetic induction HR neuron

图9 磁感应HR神经元的PSIM仿真电路

Fig.9 PSIM simulation circuit of magnetic induction HR neuron

图10 磁感应HR神经元电路产生的混沌吸引子RB= 4 kΩ (k1= -2.5) (a) vx- vy相平面; (b) vx- vφ相平面

Fig.10 Chaotic attractors generated by magnetic induction HR neuron circuit with RB=4 kΩ (k1= -2.5) (a) vx- vy phase plane; (b) vx- vφ phase plane

图11 磁感应HR神经元电路在不同磁感应强度所产生的吸引子相图(a) 周期吸引子RB=2.86 kΩ (k1=-3.5); (b) 周期吸引子RB=3.4 kΩ (k1=-3); (c) 混沌吸引子RB=4 kΩ (k1=-2.4); (d) 瞬态混沌吸引子RB=5.55 kΩ (k1=-1.8)

Fig.11 Phase plot of attractors generated by magnetic induction HR neuron circuit under different magnetic induction intensities (a) Period attractor with RB=2.86 kΩ (k1=-3.5); (b) Period attractor with RB=3.4 kΩ (k1=-3); (c) Chaotic attractor with RB=4 kΩ (k1=-2.4); (d) Transient chaotic attractor with RB=5.55 kΩ (k1=-1.8)

图12 磁感应HR神经元在不同初始电压下产生的混沌吸引子，从左至右, vz = -26π，-24π，-22π，-20π，-18π，-16π，-14π，-12π，-10π，-8π

Fig.12 Chaotic attractors generated by magnetic induction HR neuron circuit under different initial voltages, from left to right, vz = -26π, -24π, -22π, -20π, -18π, -16π, -14π, -12π, -10π, -8π

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