忆阻Rulkov神经网络同步研究

doi:10.19596/j.cnki.1001-246x.8567

摘要/Abstract

摘要：

研究电突触、化学突触以及两者共存对忆阻Rulkov神经模型集体动力学行为的影响。对于两个忆阻Rulkov神经元系统, 各种耦合方式都能使系统实现同步。对于不同的耦合强度, 神经元呈现不同的放电模式, 如方波, 三角波, 脉冲放电等。当电突触、化学突触同时存在时, 系统的同步更依赖于电耦合强度。对全局耦合忆阻Rulkov神经网络同步的研究表明: 化学突触单独作用时, 同步发生在耦合参数的某个区域范围, 当化学耦合强度超过某一阈值时, 同步会随着耦合强度的增加而被破坏。电突触单独作用时, 系统很快到达同步状态, 并且电耦合强度是决定神经元处于静止还是峰放电的关键因素, 随着电耦合强度增加, 神经元放电频率、振幅增大。当电、化学耦合同时存在时, 耦合强度的增加使神经元由静息转变为圆弧放电, 并进入同步状态。本文提供了一种通过调整耦合方式和耦合强度, 控制神经网络放电模式及其同步的可能方法。

关键词: 神经网络, 忆阻器, 电突触, 化学突触, 同步放电

Abstract:

We investigate collective dynamics of memristor Rulkov neural networks depend on electrical synapses and chemical synapses. It is found that for two memristive Rulkov neurons, the system can be synchronized regardless of coupling mode. At different coupling strengths, the neurons present different firing patterns, such as square wave, triangular wave, pulse firing, etc. As electrical synapses and chemical synapses coexist, synchronization of the system is more dependent on the strength of electrical coupling. Synchronization of globally coupled memristive Rulkov neural networks is studied. It is shown that as chemical synapses act alone, synchronization occurs within a certain region of coupling parameters. The synchronization is disrupted as the chemical coupling strength exceeds a certain threshold. As electrical synapses act alone, the system can reach a synchronized state quickly. It is also found that electrical coupling strength is the key factor to determine whether neurons are at rest or firing. As electrical coupling strength increases, firing frequency and amplitude of neuron increase. As electrical and chemical couplings coexist, the increase of coupling strength makes the neurons turn into arc discharge and reach synchronization. It provides a possible way to control firing patterns and synchronization of neural networks by adjusting coupling pattern and coupling strength.

Key words: neural network, memristor, electrical synapse, chemical synapse, synchronized firing

刘丽君, 韦笃取. 忆阻Rulkov神经网络同步研究[J]. 计算物理, 2023, 40(3): 389-400.

Lijun LIU, Duqu WEI. Synchronization of Memristive Rulkov Neural Networks[J]. Chinese Journal of Computational Physics, 2023, 40(3): 389-400.

图/表 16

图1 离散忆阻器模型的磁滞回线 (a) ω=0.01, (b) A=5

Fig.1 Pinched hysteresis loops of the discrete memristor model (a) ω=0.01, (b) A=5

图2 神经元分岔图 (a) 原始Rulkov, (b) 忆阻Rulkov (R1=0.8，R2=0.001，k=1，q0=0.1)

Fig.2 Bifurcation of neuron (a) original Rulkov model, (b) memristive Rulkov model (R1=0.8, R2=0.001, k=1, q0=0.1)

图3 不同gc值下，两个忆阻Rulkov神经元的波形 (a) gc= 0.1, (b) gc=0.29, (c) gc=0.31, (d) gc=0.38

Fig.3 Waveforms of two memristive Rulkov neurons at (a) gc=0.1, (b) gc=0.29, (c) gc=0.31, (d) gc=0.38

图4 化学突触耦合的两个忆阻Rulkov神经元的同步误差

Fig.4 Synchronization error of two memristive Rulkov neurons coupled via chemical synapses

图5 不同ge值下，两个忆阻Rulkov神经元的波形 (a) ge=0.15, (b) ge=0.35, (c) ge=0.5, (d) ge= 1

Fig.5 Waveforms of two memristive Rulkov neurons at (a) ge= 0.15, (b) ge=0.35, (c) ge=0.5, (d) ge=1

图6 通过电突触耦合的两个忆阻Rulkov神经元的同步误差

Fig.6 Synchronization error of two memristive Rulkov neurons coupled via electrical synapses

图7 通过电突触和化学突触耦合的两个忆阻Rulkov模型的同步误差

Fig.7 Synchronization error of two memristive Rulkov models coupled via both electrical and chemical synapses

图8 不同gc值下，神经元(i = 10、30、50、70、90)的波形，ge= 0.001

Fig.8 Waveforms of neurons (i = 10, 30, 50, 70, 90) at different gc with ge= 0.001

图9 不同gc值下，网络的空间模式，ge= 0.001 (a) gc= 0.001, (b) gc = 0.16, (c) gc= 0.3, (d) gc= 0.4

Fig.9 Developed spatial patterns of network at different gc with ge= 0.001 (a) gc= 0.001, (b) gc = 0.16, (c) gc = 0.3, (d) gc = 0.4

图10 固定gc= 0.001，化学突触全局耦合的忆阻Rulkov模型的同步误差

Fig.10 Synchronization error of memristive Rulkov models for global coupling of chemical synapses with gc=0.001

图11 不同ge值下，神经元(i = 10、30、50、70、90)的波形(gc= 0.001)

Fig.11 Waveforms of neurons (i = 10, 30, 50, 70, 90) at different ge with gc= 0.001

图12 不同ge值下，网络的空间模式(gc= 0.001) (a) ge= 0.08, (b) ge= 0.15, (c) ge= 0.3, (d) ge= 0.7

Fig.12 Developed spatial patterns of network at different ge with gc= 0.001 (a) ge= 0.08, (b) ge= 0.15, (c) ge=0.3, (d) ge= 0.7

图13 固定ge= 0.001，电突触全局耦合的忆阻Rulkov模型的同步误差

Fig.13 Synchronization error of memristive Rulkov models for global coupling of chemical synapses with ge= 0.001

图14 不同ge、 gc值下，神经元(i = 10、30、50、70、90)的波形 (a) ge= 0.02、gc= 0.01，(b) ge= 0.1、gc= 0.075，(c) ge= 0.12、gc= 0.062，(d) ge= 0.15、gc= 0.05

Fig.14 The waveforms of neurons (i = 10, 30, 50, 70, 90) for different ge and gc (a) ge= 0.02、gc= 0.01, (b) ge= 0.1、gc= 0.075, (c) ge= 0.12、gc= 0.062, (d) ge= 0.15、gc= 0.05

图15 不同ge、gc值下，网络的空间模式 (a) ge= 0.02、gc= 0.01，(b) ge= 0.1、gc= 0.075，(c) ge= 0.12、gc= 0.062，(d) ge= 0.15、gc= 0.05

Fig.15 Developed spatial patterns of network for different ge and gc (a) ge= 0.02、gc= 0.01, (b) ge= 0.1、gc= 0.075, (c) ge= 0.12、gc= 0.062, (d) ge= 0.15、gc= 0.05

图16 电突触和化学突触共存全局耦合忆阻Rulkov模型的同步误差

Fig.16 Synchronization error of globally coupled memristive Rulkov models co-existing electrical and chemical synapses

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