电磁辐射下正切型忆阻Hindmarsh-Rose神经网络的动力学研究

doi:10.19596/j.cnki.1001-246x.8847

摘要/Abstract

摘要：

通过磁控忆阻器的感应电流模拟电磁辐射, 研究电磁辐射效应下Newman-Watts(NW)小世界的正切型忆阻耦合Hindmarsh-Rose(HR)神经网络动力学行为。数值仿真发现: 增大耦合强度会促进神经元之间的同步和改变神经元的放电模式; 当电磁辐射效应作用时, 神经网络对初始值敏感, 同时通过哈密顿能量发现, 电磁辐射会增强神经元放电所需能量。当忆阻耦合与电磁辐射效应共同作用时, 电磁辐射强度越小, 忆阻耦合更能有效地促进网络同步。实验结果表明: 在电磁辐射效应下的正切型忆阻耦合神经网络对初始值状态敏感, 神经网络的同步行为和放电活动与耦合强度、电磁辐射有关。

关键词: Hindmarsh-Rose神经元, 电磁辐射效应, 正切型忆阻, 同步放电

Abstract:

The electromagnetic environment around neurons is very complex, and it is important to study the effect of electromagnetic radiation on neuronal behavior. Electromagnetic radiation is simulated by the induced current of a magnetically controlled memristor to study the behavior of tangent-type memristor-coupled Hindmarsh-Rose (HR) neural network dynamics in a small world of NW under the effect of electromagnetic radiation. Numerical simulations have found that increasing the coupling strength promotes synchronization between neurons and alters their firing pattern; the neural network is sensitive to the initial value when the electromagnetic radiation effect is in effect, and it is also found that electromagnetic radiation enhances the energy required for neuronal firing by Hamiltonian energy. When amnesic coupling and electromagnetic radiation effect act together, the smaller the intensity of electromagnetic radiation, the more effective amnesic coupling can promote network synchronization. The experimental results show that the tangent-type amnesia-coupled neural network under the effect of electromagnetic radiation is sensitive to the state of the initial value, and the synchronization behavior and discharge activity of the neural network are related to the coupling strength and electromagnetic radiation.

Key words: Hindmarsh-Rose neurons, electromagnetic radiation effects, tangential amnesia, synchronized discharge

代志伟, 韦笃取. 电磁辐射下正切型忆阻Hindmarsh-Rose神经网络的动力学研究[J]. 计算物理, 2025, 42(2): 243-252.

Zhiwei DAI, Duqu WEI. Dynamics of Tangent-type Memory Hindmarsh-Rose Neural Networks under Electromagnetic Radiation[J]. Chinese Journal of Computational Physics, 2025, 42(2): 243-252.

图/表 9

图1 不同k1值下两个忆阻HR神经元(i=40、80)的时间序列和相位图(k2=0) (a)、(d) k1=0.001；(b)、(e) k1=0.01；(c)、(f) k1=0.02

Fig.1 Time series and phase diagrams of two memristor at different k1 with HR neurons (i=40, 80) (k2=0) (a)、(d) k1=0.001;(b)、(e) k1=0.01;(c)、(f) k1=0.02

图2 不同k1值下，HR神经网络的空间模式(k2=0) (a) k1=0.001；(b) k1=0.01；(c) k1=0.02

Fig.2 Spatial mode of HR neural network at different k1 (k2=0) (a) k1=0.001; (b) k1=0.01; (c) k1=0.02

图3 不同记忆参数α值下HR神经网络的同步性(β=1)

Fig.3 Synchronization of HR neural networks at different memory parameter α (β=1)

图4 不同k2值下两个忆阻HR神经元(i =40、80)的时间序列和相位图(k1=0)(a)、(d) k2=0.3；(b)、(e) k2=0.4；(c)、(f) k2=0.5

Fig.4 Time series and phase diagrams of two memristor HR neurons at different k2 (i=40, 80, k1=0)(a) and (d) k2=0.3;(b) and (e) k2=0.4;(c) and (f) k2=0.5

图5 不同k2值下，HR神经网络的空间模式(k1=0) (a) k2=0.3；(b) k2=0.4；(c) k2=0.5

Fig.5 Spatial mode of HR neural network at different k2 (k1=0) (a) k2=0.3; (b) k2=0.4; (c) k2=0.5

图6 神经元状态切换(k1=0，k2=0.3，ϕ1=1) (a)非负最大值分岔图；(b) ϕ2=-0.5，神经元膜电位时间序列；(c) ϕ2=-0.4，神经元膜电位时间序列

Fig.6 State switching with k1=0, k2=0.3, ϕ1=1 (a) non-negative maximum bifurcation diagram; (b) neuron membrane potential time series at ϕ2=-0.5; (c) neuron membrane potential time series at ϕ2=-0.4

图7 时序图对应的哈密顿能量图(a)神经元膜电位时间序列；(b)哈密顿能量图

Fig.7 Timing diagrams corresponding to Hamiltonian energy diagrams (a)nneuron membrane potential time series; (b)Hamilton energy map

图8 两参数区域下(k1-k2)的同步因子(a) ϕ2=1; (b) ϕ2=-1

Fig.8 Synchronization factor of (k1-k2) at two-parameters (a) ϕ2=1; (b) ϕ2=-1

图9 两参数区域下(k1-k2)的标准差σ (a) ϕ2=1；(b) ϕ2=-1

Fig.9 The standard deviation of (k1-k2) σ at two-parameters (a) ϕ2=1; (b) ϕ2=-1

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