约瑟夫森结作用下神经元的动力学特性分析

doi:10.19596/j.cnki.1001-246x.8667

摘要/Abstract

摘要：

将约瑟夫森结引入Hindmarsh-Rose(HR)神经元中, 构建具有约瑟夫森结的四维神经元模型。首先通过理论分析得出系统的耗散性以及平衡点的稳定性; 再通过调控约瑟夫森结参数观察电耦合系统的分岔情况, 发现系统在合适的参数范围内表现出倍周期分岔、含混沌的加周期分岔等丰富的动力学特性; 并在化学突触作用下构建全局耦合神经元网络, 通过同步因子刻画系统在不同参数下的同步程度, 发现耦合强度和约瑟夫森结参数能够影响系统的放电同步状态。

关键词: 约瑟夫森结, 耦合, 平衡点, 放电分岔, 同步

Abstract:

A four-dimensional neuron model with Josephson junction is constructed by introducing Josephson junction into HR neuron. Firstly, the dissipative property of the system and the stability of the equilibrium point are obtained through theoretical analysis. By adjusting the Josephson junction parameters to observe the bifurcation of the electric-coupled system, it is found that the system shows rich dynamic characteristics such as period-doubling bifurcation and addition-period bifurcation including chaos within the appropriate parameter range. A global coupled neural network is constructed under the action of chemical synapses. Synchronization factors are used to describe the synchronization degree of the system under different parameters. It is found that coupling strength and Josephson junction parameters can affect the discharge synchronization state of the system.

Key words: Josephson junction, coupling, equilibrium point, discharge bifurcation, synchronous

中图分类号:

O193
O441.3

肖彤彤, 李新颖, 钱雨晴. 约瑟夫森结作用下神经元的动力学特性分析[J]. 计算物理, 2023, 40(6): 752-760.

Tongtong XIAO, Xinying LI, Yuqing QIAN. Dynamic Analysis of Neurons by Josephson Junction[J]. Chinese Journal of Computational Physics, 2023, 40(6): 752-760.

图/表 9

图1 系统在不同参数下的分岔图(a)参数k; (b)参数χ0(k=0.1); (c)参数χ0(k=0.2)

Fig.1 Bifurcation diagrams of the system under different parameters (a) k; (b) χ0(k=0.1); (c) χ0(k=0.2)

图2 不同k值所对应的平面相图(a) k=-0.7；(b) k=-0.1；(c) k=0.2

Fig.2 Phase diagram to different values of k (a) k=-0.7; (b) k=-0.1; (c) k=0.2

图3 双参数分岔图(a)g和χ0；(b)r和k；(c)r和χ0

Fig.3 Two-parameter bifurcation diagram (a) g and χ0; (b) r and k; (c) r and χ0

图4 不同参数k下耦合强度D的相似函数图(a) k=0.2; (b) k=-0.2

Fig.4 Similar function diagram of coupling strength D in different parameters k (a) k=0.2; (b) k=-0.2

图5 系统在不同耦合强度D下的时间历程图和相图(a)、(d) D=0.1；(b)、(e) D=0.2；(c)、(f) D=0.6

Fig.5 Time history diagram and phase diagram of the system under different coupling strength D at k=0.2 (a) and (d) D=0.1; (b) and (e) D=0.2; (c) and (f) D=0.6

图6 不同耦合强度下，系统关于r和χ0的双参数相似函数图(a) D=0.5; (b) D=0.2

Fig.6 The two-parameter similar function graph of r and χ0 under different coupling strength (a) D=0.5; (b) D=0.2

图7 不同参数下的同步因子(a) 系统随参数D变化的同步趋势; (b) 系统随参数k变化的同步趋势

Fig.7 Synchronization factor plot of different parameters (a) synchronization trend of the system with D; (b) synchronization trend of the system with k

图8 系统在不同k值时的时间历程图和相图(a)、(c) k=0.2; (b)、(d) k=0.8

Fig.8 Time history diagram and phase diagram of the system under different k values (a) and (c) k=0.2; (b) and (d) k=0.8

图9 不同k值下，系统关于r和χ0的双参数同步因子图(a)、(c) k=0.1; (b)、(d) k=0.5

Fig.9 Two-parameter synchronization factor diagram of r and χ0 at different k (a) and (c) k=0.1; (b) and (d) k=0.5

参考文献 24

1	HODGKIN A L , Huxley A F . A quantitative description of membrane current and its application to conduction and excitation in nerve[J]. The Journal of Physiology, 1952, 117 (4): 500- 544. DOI
2	MORRIS C , LECAR H . Voltage oscillations in the barnacle giant muscle fiber[J]. Biophysical Journal, 1981, 35 (1): 193- 213. DOI
3	HINDMARSH J L , ROSE R M . A model of neuronal bursting using three coupled first order differential equations[J]. Proceedings of the Royal Society B: Biological Sciences, 1984, 221 (1222): 87- 102.
4	CHAY T R , FAN Y S , LEE Y S . Bursting, spiking, chaos, fractals and universality in biological rhythms[J]. International Journal of Bifurcation & Chaos, 1995, 5 (3): 595- 635.
5	杨腾云, 李新颖, 高月月. 电磁辐射下神经元放电模式及其环状耦合同步转迁[J]. 四川大学学报(自然科学版), 2021, 58 (1): 014002.
6	魏梦可, 韩修静, 张晓芳, 等. 正负双向脉冲式爆炸及其诱导的簇发振荡[J]. 力学学报, 2019, 51 (3): 904- 911.
7	WANG G W , WU Y , XIAO F L , et al. Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction[J]. Physica A: Statistical Mechanics and Its Applications, 2022, 598, 127274. DOI
8	丁学利, 李玉叶. 具有时滞的抑制性自突触诱发的神经放电的加周期分岔[J]. 物理学报, 2016, 65 (21): 210502. DOI
9	李宁, 李新颖, 杨腾云. 电磁感应下胰腺β细胞的放电及同步分析[J]. 云南大学学报(自然科学版), 2021, 43 (2): 280- 289.
10	PHAN C , YOU Y C . Synchronization of boundary coupled Hindmarsh-Rose neuron network[J]. Nonlinear Analysis: Real World Applications, 2020, 55, 103139. DOI
11	WU K J , WANG T J . Study on electrical synapse coupling synchronization of Hindmarsh-Rose neurons under Gaussian white noise[J]. Neural Computing & Applications, 2018, 30 (2): 551- 561.
12	XIE Y , YAO Z , MA J . Phase synchronization and energy balance between neurons[J]. Frontiers of Information Technology& Electronic Engineering, 2022, 23 (9): 1407- 1420.
13	LIU Y , XU W J , MA J . A new photosensitive neuron model and its dynamics[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21 (9): 1387- 1396.
14	GOLUBOV A A , KUPRIYANOV M Y . The current-phase relation in Josephson junctions[J]. Reviews of Modern Physics, 2004, 76 (2): 411- 469. DOI
15	CROTTY P , SCHULT D , SEGALL K . Josephson junction simulation of neurons[J]. Physical Review E, 2010, 82 (1): 011914. DOI
16	LEI Y M , FU R . Heteroclinic chaos in a Josephson-junction system perturbed by dichotomous noise excitation[J]. EPL(Europhysics Letters), 2015, 112 (6): 60005. DOI
17	OCTAVIO M . Chaos and thermally-induced chaos in Josephson junction devices and circuits[J]. Physica A: Statistical Mechanics and Its Applications, 1990, 163 (1): 248- 257.
18	ZHANG Y , ZHOU P , TANG J . Mode selection in a neuron driven by Josephson junction current in presence of magnetic field[J]. Chinese Journal of Physics, 2021, 71, 72- 84.
19	NJITACKE Z T , RAMAKRISHNAN B , RAJAGOPAL K , et al. Extremely rich dynamics of coupled heterogeneous neurons through a Josephson junction synapse[J]. Chaos, Solitons & Fractals, 2022, 164, 112717.
20	TANG L H , HE Z M , YAO Y L . Magnetic induction HR neuron with hidden extreme multistability and its circuit implementation[J]. Chinese Journal of Computational Physics, 2022, 39 (5): 589- 597.
21	TANG L H , HE Z M , YAO Y L . Dynamical analysis and circuit implementation of a memristive Hopfield neural network[J]. Chinese Journal of Computational Physics, 2022, 39 (2): 244- 252.
22	LIU D , YANG F , ZHOU G , et al. Dynamical behavior analysis of a class of 4D memristive chaotic systems[J]. Chinese Journal of Computational Physics, 2018, 35 (4): 458- 468.
23	马娟娟, 李新颖, 杨宗凯, 等. 磁感应下Chay神经元的簇发与同步转迁[J]. 中国医学物理学杂志, 2022, 4 (39): 484- 492.
24	WANG C N , TANG J , MA J . Minireview on signal exchange between nonlinear circuits and neurons via field coupling[J]. The European Physical Journal Special Topics, 2019, 228 (10): 1907- 1924.

[1]	邵贝贝, 邹艳丽, 洪少燕, 梁婵娟. 基于复杂网络拓扑的电网Braess悖论现象研究[J]. 计算物理, 2023, 40(6): 770-778.
[2]	李德奎, 毛北行. 时滞干扰环状网络的修正函数投影同步及仿真[J]. 计算物理, 2023, 40(5): 643-652.
[3]	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.
[4]	曹文鑫, 韦笃取. 基于NG-RC电机系统的混沌预测[J]. 计算物理, 2023, 40(4): 519-526.
[5]	方锋, 周文长, 罗长杰, 李煜璠, 杨杰. 超冷等离子体演化早期的离子温度与库仑耦合强度[J]. 计算物理, 2023, 40(3): 275-281.
[6]	马秀宝, 崔国民, 周志强, 肖媛, 徐玥, 杨其国. 带有个体淘汰的强制进化随机游走算法优化质量交换网络[J]. 计算物理, 2023, 40(3): 376-388.
[7]	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.
[8]	李震波, 唐叶芝. 高维混沌系统的多元函数投影同步及其保密通信方案[J]. 计算物理, 2023, 40(1): 91-105.
[9]	高正, 邹艳丽, 胡均万, 姚高华, 刘唐慧美. 基于复杂网络理论的电网耦合强度分配策略[J]. 计算物理, 2022, 39(5): 579-588.
[10]	刘凯歌, 韦笃取. 基于WOA-ESN的电机系统混沌振荡预测[J]. 计算物理, 2022, 39(4): 498-504.
[11]	张少泽, 邹艳丽, 谭秫毅, 李浩乾, 刘欣妍. 基于复杂网络理论的互联电网Braess悖论现象分析[J]. 计算物理, 2022, 39(2): 233-243.
[12]	颜闽秀, 徐辉. 共存吸引子个数可调的混沌系统[J]. 计算物理, 2021, 38(2): 244-252.
[13]	曹启伟, 肖德龙, 杨显俊, 王建国. 磁瑞利-泰勒不稳定性非线性演化数值模拟[J]. 计算物理, 2021, 38(1): 5-15.
[14]	李玉山. 偶极相互作用对自旋轨道耦合自旋-1凝聚体中磁畴分布的影响[J]. 计算物理, 2021, 38(1): 120-126.
[15]	周倩, 韦笃取. 场耦合忆阻神经网络的电活动[J]. 计算物理, 2020, 37(6): 750-756.