电磁场耦合忆阻Izhikevich神经网络电活动研究

doi:10.19596/j.cnki.1001-246x.8582

摘要/Abstract

摘要：

考虑到电磁场的影响, 在Izhikevich神经元模型中引入电场变量和磁通变量, 利用电突触耦合构建神经网络, 研究电磁场耦合忆阻Izhikevich神经网络集体动力学行为。数值仿真发现: 随着电突触耦合强度的增大, 神经网络逐渐达到同步状态, 并且神经元的放电模式也会随之改变。增大磁场耦合值可以提高神经元的放电活性, 并且对网络同步也有一定的促进作用, 而增大电场则会抑制神经元的放电活动。另外, 当电突触与磁场耦合共同作用时, 磁场耦合值越小, 电突触耦合更能有效促进网络同步; 在电突触耦合强度的作用下, 电场抑制电活动的效果更明显。研究结果可望为理解神经系统中的信号编码和传递提供新的见解。

关键词: Izhikevich神经元, 电突触, 电磁感应, 同步

Abstract:

The electrophysiological environment inside and outside the neuron will generate an electric field due to the transmission and concentration of ions, which will then excite the magnetic field, and the formed electromagnetic field will work together to regulate the electrical activity of the neuron. Therefore, considering the influence of electromagnetic field, this paper introduces electric field variables and magnetic flux variables into the traditional neuron model and uses electrical synaptic coupling to construct neuron network, then studies the collective dynamic behavior of memristive Izhikevich neural network under electromagnetic field coupling. Through numerical simulation, it is found that the increase of the electrical synaptic coupling value will change the firing pattern of neurons, and make the neural network achieve synchronization. Increasing the coupling value of magnetic field can increase the firing activity of neurons, and have a beneficial effect on the network synchronization, while increasing the electric field can inhibit the electrical activity of neurons. In addition, when electrical synaptic and magnetic field coupling work together, the smaller value of the magnetic field coupling, the more effective the electrical synaptic coupling can promote network synchronization. The electric field is more effective in suppressing electrical activity given the strength of the electrical synaptic coupling. The findings are expected to provide new perspectives for understanding signal encoding and transmission in the nervous system.

Key words: Izhikevich neuron, electrical synapse, electromagnetic induction, synchronization

陆丽梅, 韦笃取. 电磁场耦合忆阻Izhikevich神经网络电活动研究[J]. 计算物理, 2023, 40(4): 490-499.

Limei LU, Duqu WEI. Firing Activity of Memristive Izhikevich Neural Network Under Electromagnetic Field Coupling[J]. Chinese Journal of Computational Physics, 2023, 40(4): 490-499.

图/表 9

图1 不同gb值下，神经元(i=40, 160)放电活动，gc=0，r=0。(a)~(c)分别为gb=0.005，0.015，0.05时神经元的膜电位时间序列；(d)~(f)分别为gb=0.005，0.015，0.05时神经元的相平面图。

Fig.1 The firing activity of neurons (i=40, 160) for different gb with gc=0, r=0. (a)~(c) are the time series of membrane potential of neurons when gb=0.005, 0.015, 0.05, respectively. (d)~(f) are the phase plans of neurons when gb=0.005, 0.015, 0.05, respectively.

图2 不同gb值下，神经网络时空图(gc=0，r=0) (a)gb=0.005；(b)gb=0.015；(c)gb=0.05

Fig.2 Developed spatial patterns of network for different gb with gc=0, r=0 (a)gb=0.005; (b)gb=0.015; (c)gb=0.05

图3 不同gc值下，神经元(i=40, 160)放电活动，gb=0，r=0。(a)~(c)分别为gc=0.005，0.01，0.1时神经元的膜电位时间序列；(d)~(f)分别为gc=0.005，0.01，0.1时神经元的相平面图。

Fig.3 The firing activity of neurons (i=40, 160) for different gc with gb=0, r=0. (a)~(c) are the time series of membrane potential of neurons when gc=0.005, 0.01, 0.1, respectively; (d)~(f) are the phase plans of neurons when gc=0.005, 0.01, 0.1, respectively.

图4 不同gc值下，神经网络时空图(gb=0，r=0) (a)gc=0.005；(b)gc=0.01；(c)gc=0.1

Fig.4 Developed spatial patterns of network for different gc with gb=0, r=0 (a)gc=0.005; (b)gc=0.01; (c)gc=0.1

图5 在双参数区域(gb-gc)下计算同步因子R

Fig.5 Degree of synchronization computed in the two-parameter space (gb-gc)

图6 不同r值下，神经元(i=40, 160)的膜电位时间序列(gb=0.02，gc=0.01) (a) r=0.000 01；(b) r=0.000 05；(c) r=0.000 08；(d) r=0.000 1

Fig.6 The time series of membrane potential of neurons(i=40, 160) for different r with gb=0.02, gc=0.01 (a) r=0.000 01; (b) r=0.000 05; (c) r=0.000 08; (d) r=0.000 1

图7 不同r值下，神经网络的时空图(gb=0.02，gc=0.01) (a) r=0.000 01；(b) r=0.000 05；(c) r=0.000 08；(d) r=0.000 1

Fig.7 Developed spatial patterns of network for different r with gb=0.02, gc=0.01 (a) r=0.000 01; (b) r=0.000 05; (c) r=0.000 08; (d) r=0.000 1

图8 在双参数区域下计算标准差σ (a) r-gb；(b) r-gc

Fig.8 Degree of standard deviation computed in the two-parameter space (a)r-gb; (b)r-gc

图9 在双参数区域(r-gb)下计算同步因子R

Fig.9 Degree of synchronization computed in the two-parameter space (r-gb)

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