随机边界诱导Izhikevich神经元网络的时空模式转换

doi:10.19596/j.cnki.1001-246x.8632

摘要/Abstract

摘要：

在随机边界条件下构建由200 × 200个Izhikevich神经元组成的方形网络, 并利用计算机模拟计算方形网络的时空特性和同步因子, 对神经元的放电模式、分岔现象以及方形网络的时空模式和同步性质进行研究。研究结果表明: 在相同电流刺激和耦合强度下, 由不同放电模式Izhikevich神经元构建的方形网络中, 仅当神经元处于Regular Spiking放电模式下才能在网络中观察到螺旋波种子的出现和消失; 对于其他放电模式(Fast Spiking, Chattering和Intrinsically Bursting)的Izhikevich神经元构建的方形网络, 则无法观察到螺旋波种子的出现。当外界电流刺激恒定时, 只有当神经元之间的耦合强度为中等大小时才可在方形网络中观察到螺旋波种子的出现和消亡, 相对较小或较大的耦合强度不能诱导神经元网络出现螺旋波种子。对方形神经网络中的同步因子研究发现同步因子随耦合强度的变化存在类似"反共振"的形式。

关键词: 螺旋波, 时空, 神经元, 随机, 网络, 模式转换

Abstract:

Izhikevich neuronal model is based on the modeling of cortical and thalamic neurons. This model has the characteristics of being closer to the discharge properties of real biological neurons and it is convenient for large-scale simulation. A square neural network composed of 200 × 200 Izhikevich neurons is constructed under random boundary conditions in this paper, the computer simulation method is used to calculate the spatiotemporal characteristics and synchronization factor of the square network, and the firing patterns and bifurcation phenomena of neurons, as well as the spatiotemporal patterns and synchronization properties of the square network are studied. The results show that in the square neural network constructed by Izhikevich neurons with different discharge modes under the same current stimulation and coupling intensity, the emergence and disappearance of spiral wave seeds can be observed in the neural network only when the neurons are in the Regular Spiking discharge mode. On the other hand, spiral wave seeds cannot be observed in the square neural network constructed by Izhikevich neurons with other discharge modes (e.g. Fast Spiking, Chattering, Internally Bursting). When the external current stimulation is constant, only the medium-sized coupling strength between neurons can induce the emergence and extinction of spiral wave seeds in the square neural network, and smaller or larger coupling strength cannot induce spiral wave seeds in the neural network. In addition, the synchronization factor in square neural networks has been investigated.

Key words: spiral waves, spatiotemporal, neurons, stochastic, networks, mode transformation

王国威, 付燕. 随机边界诱导Izhikevich神经元网络的时空模式转换[J]. 计算物理, 2023, 40(5): 622-632.

Guowei WANG, Yan FU. Stochastic Boundary-induced Spatiotemporal Pattern Transformation in Izhikevich Neuronal Networks[J]. Chinese Journal of Computational Physics, 2023, 40(5): 622-632.

图/表 11

表1 不同放电类型神经元对应的控制参数

Table 1 Control parameters of neurons with different discharge types

Types	a	b	c	d
RS	0.02	0.2	-65	8
FS	0.10	0.2	-65	2
CH	0.02	0.2	-50	2
IB	0.02	0.2	-55	4

图1 神经元耦合连接示意图

Fig.1 Schematic diagram of neuron coupling connection

图2 200×200方形网络连接示意图

Fig.2 Schematic diagram of 200×200 square network

图3 不同类型Izhikevich神经元模型的放电序列图(a) a = 0.02, b = 0.2, c = -50.0, d = 2.0, I = 10;(b) a = 0.1, b = 0.2, c = -65.0, d = 2.0, I = 10; (c) a = 0.02, b = 0.2, c = -55.0, d = 4.0, I =10;(d) a = 0.02, b = 0.2, c = -65.0, d = 8.0, I = 10

Fig.3 Time series diagram of membrane potential of different types of Izhikevich neuron models (a) a = 0.02, b = 0.2, c = -50.0, d = 2.0, I = 10; (b) a = 0.1, b = 0.2, c = -65.0, d = 2.0, I = 10; (c) a = 0.02, b = 0.2, c = -55.0, d = 4.0, I =10; (d) a = 0.02, b = 0.2, c = -65.0, d = 8.0, I = 10

图4 4种不同放电模式的相图(a) a = 0.02, b = 0.2, c = -50.0, d = 2.0, I = 10; (b) a = 0.1, b = 0.2, c = -65.0, d = 2.0, I = 10; (c) a = 0.02, b = 0.2, c = -55.0, d = 4.0, I =10;(d) a = 0.02, b = 0.2, c = -65.0, d = 8.0, I = 10

Fig.4 Phase diagrams of four different discharge modes (a) a = 0.02, b = 0.2, c = -50.0, d = 2.0, I = 10;(b) a = 0.1, b = 0.2, c = -65.0, d = 2.0, I = 10; (c) a = 0.02, b = 0.2, c = -55.0, d = 4.0, I =10;(d) a = 0.02, b = 0.2, c = -65.0, d = 8.0, I = 10

图5 4种不同类型Izhikevich神经元的膜电位随外界刺激电流变化的分叉图(a) a = 0.02, b = 0.2, c = -65.0, d = 8.0; (b) a = 0.1, b = 0.2, c = -65.0, d = 2.0; (c) a = 0.02, b = 0.2, c = -50.0, d = 2.0; (d) a = 0.02, b = 0.2, c = -55.0, d = 4.0

Fig.5 Bifurcation diagram of the membrane potential of four different types of Izhikevich neurons with external stimulation current (a) a = 0.02, b = 0.2, c = -65.0, d = 8.0; (b) a = 0.1, b = 0.2, c = -65.0, d = 2.0;(c) a = 0.02, b = 0.2, c = -50.0, d = 2.0; (d) a = 0.02, b = 0.2, c = -55.0, d = 4.0

图6 3 000时间单位时改变耦合强度D时随机边界诱导的时空模式转换(a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10) (a)~(i) D = 0.0, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0

Fig.6 Spatiotemporal pattern transformation induced by random boundary when changing coupling strength D at 3 000 time units (a = 0.02, b = 0.2, c = -65.0, d = 8.0, I = 10) (a)~(i) D = 0.0, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0

图7 5 000时间单位时改变耦合强度D时随机边界诱导的时空模式转换(a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10) (a)~(i) D = 0.3, 0.6, 0.9, 1.0, 1.2, 1.5, 1.8, 2.0, 2.1

Fig.7 Spatiotemporal pattern transformation induced by random boundary when changing coupling strength D at 5 000 time unit (a = 0.02, b = 0.2, c = -65.0, d = 8.0, I = 10) (a)~(i) D = 0.3, 0.6, 0.9, 1.0, 1.2, 1.5, 1.8, 2.0, 2.1

图8 D = 1.0时不同时间单位下随机边界诱导的时空模式转换(a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10) (a)~(i) t = 50, 500, 1 000, 1 500, 2 000, 2 500, 3 000, 3 500, 4 000

Fig.8 Spatiotemporal pattern transformation induced by random boundary at different time units when D = 1.0 (a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10) (a)~(i) t = 50, 500, 1 000, 1 500, 2 000, 2 500, 3 000, 3 500, 4 000

图9 3 000时间单位时方形神经网络对应的同步因子随耦合强度D变化的图像(a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10)

Fig.9 Synchronization factor corresponding to the square neural network changing with coupling strength D at 3 000 time units (a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10)

图10 5 000时间单位时方形神经网络对应的同步因子随耦合强度D变化的图像(a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10)

Fig.10 Synchronization factor corresponding to the square neural network changes with coupling strength D at 5 000 time units (a = 0.02, b = 0.2, c = -65.0, d = 8.0, I =10)

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