复杂网络上耦合神经系统的非聚类相同步

谢一丁; 王征平; 刘帅

doi:10.21656/1000-0887.400297

复杂网络上耦合神经系统的非聚类相同步

doi: 10.21656/1000-0887.400297

¹武汉理工大学能源与动力工程学院, 武汉 430063;²武汉理工大学理学院, 武汉 430070;³西北农林科技大学理学院, 陕西杨凌 712100

基金项目: 国家自然科学基金（11605142；11871386）

详细信息

作者简介:
谢一丁（1999—），男(E-mail: xyd@whut.edu.cn)；王征平（1979—），男，教授(E-mail: zpwang@whut.edu.cn)；刘帅（1987—），男，副教授(通讯作者. E-mail: liushuai0109@mails.ucas.ac.cn).

中图分类号: O193
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- 被引次数: 0
出版历程
- 收稿日期: 2019-10-10
- 修回日期: 2019-11-26
- 刊出日期: 2020-06-01

Networked Non-Clustering Phase Synchronization in Coupled Neuron Systems

¹School of Energy and Power Engineering, Wuhan University of Technology, Wuhan 430063, P.R.China;²School of Science, Wuhan University of Technology, Wuhan 430070, P.R.China;³College of Science, Northwest A&F University, Yangling, Shaanxi 712100, P.R.China

Funds: The National Natural Science Foundation of China（11605142；11871386）

摘要

摘要: 考虑了不同复杂网络结构（小世界、无标度和随机网络）条件下的耦合神经元系统，针对其进入相同步的同步化路径进行了建模与仿真，发现系统呈现出非聚类相同步现象，并对其形成原因进行了定性分析.结果表明:复杂网络上的耦合神经元系统与其在规则网络下有相同的同步行为，系统均不出现通常耦合相振子中的聚类成群现象，而表现为随着耦合强度的增加所有神经元渐进趋于同步.另外，随着放电尖峰的插入与弥合，最终导致系统个体平均频率先增强后衰减的变化.这些结果将丰富对于网络动力学行为（尤其是相同步）的认识，对理解神经认知科学具有一定意义.
- 非聚类相同步 /
- 耦合神经元 /
- 复杂网络 /
- 聚类相同步
Abstract: The phase synchronization of coupled neurons under different complex network environments (including classical small-world, scale-free and random networks) was studied. Differing from the clustering phase synchronization in coupled phase oscillators generally found and reported in previous literature, a novel non-clustering phase synchronization was uncovered. The global synchronization involves 2 different dynamical processes: the frequency increase and the frequency decrease, where the frequency increase is induced by the spike insertion, and the frequency decrease is induced by the spike merge. Therefore, the neuron’s frequency variation mainly depends on the change of spike numbers, and the usual phase clustering phenomenon cannot be found here. The findings could enrich the understanding of networked dynamical behaviors including the phase synchronization and the computational neuron dynamics.
- non-clustering phase synchronization /
- coupled neurons /
- complex network /
- clustering phase synchronization

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参考文献(18)

[1]	ARENAS A, DAZ-GUILERA A, KURTHS J, et al. Synchronization in complex networks[J]. Physics Reports,2008,469(3): 93-153.
[2]	TANG Y, QIAN F, GAO H, et al. Synchronization in complex networks and its application: a survey of recent advances and challenges[J]. Annual Reviews in Control,2014,38(2): 184-198.
[3]	PECORA L M, CARROLL T L, JOHNSON G A, et al. Fundamentals of synchronization in chaotic systems, concepts, and applications[J]. Chaos,1997, 7(4): 520-543.
[4]	ROSENBLUM M G, PIKOVSKY A S, KURTHS J. Phase synchronization of chaotic oscillators[J]. Physical Review Letters,1996,76(11): 1804-1807.
[5]	ZHENG Z G, HU G, HU B B. Phase slips and phase synchronization of coupled oscillators[J]. Physical Review Letters,1998,81(24): 5318-5321.
[6]	郑志刚, 胡岗, 周昌松, 等. 耦合混沌系统的相同步: 从高维混沌到低维混沌[J]. 物理学报, 2000,49(12): 2320-2327.(ZHENG Zhigang, HU Gang, ZHOU Changsong, et al. Phase synchronization in coupled chaotic systems: transitions from high-to low-dimensional chaos[J]. Acta Physica Sinica,2000,49(12): 2320-2327.(in Chinese))
[7]	ZHAN M, ZHENG Z G, HU G, et al. Nonlocal chaotic phase synchronization[J]. Physical Review E,2000,62(3): 3552-3557.
[8]	GOMEZ-GARDENES J, MORENO Y, ARENAS A. Paths to synchronization on complex networks[J]. Physical Review Letters,2007,98(3): 034101. DOI: 10.1103/PhysRevLett.98.034101.
[9]	CHIANG W Y, LAI P Y, CHAN C K. Frequency enhancement in coupled noisy excitable elements[J]. Physical Review Letters,2011,106(25): 254102. DOI: 10.1103/PhysRevLett.106.254102.
[10]	LIU S, ZHAN M. Clustering versus non-clustering phases synchronizations[J]. Chaos,2014,24(1): 013104. DOI: 10.1063/1.4861685.
[11]	LIU S, HE Z W, ZHAN M. Firing rates of coupled noisy excitable elements[J]. Frontiers of Physics,2014,9(1): 120-127.
[12]	张玮玮, 陈定元, 吴然超, 等. 一类基于忆阻器分数阶时滞神经网络的修正投影同步[J]. 应用数学和力学, 2018,39(2): 239-248.(ZHANG Weiwei, CHEN Dingyuan, WU Ranchao, et al. Modified-projective-synchronization of memristor-based fractional-order delayed neural networks[J]. Applied Mathematics and Mechanics,2018,39(2): 239-248.(in Chinese))
[13]	李天择, 郭明, 陈向勇, 等. 基于多切换传输的复变量混沌系统的有限时组合同步控制[J]. 应用数学和力学, 2019,40(11): 1299-1308.(LI Tianze, GUO Ming, CHEN Xiangyong, et al. Finite-time combination synchronization control of complex-variable chaotic systems with multi-switching transmission[J]. Applied Mathematics and Mechanics,2019,40(11): 1299-1308.(in Chinese))
[14]	HUANG Z, ZHAN M, LI F, et al. Single-clustering synchronization in a ring of Kuramoto oscillators[J]. Journal of Physics A: Mathematical and Theoretical,2014,47(12): 125101. DOI: 10.1088/1751-8113/47/12/125101.
[15]	WATTS D J ,STROGATZ S H. Collective dynamics of ‘small-world’ networks[J]. Nature,1998,393(6684): 440-442.
[16]	BARABASI A L, ALBERT R. Emergence of scaling in random networks[J]. Science,1999,286(5439): 509-512.
[17]	STROGATZ S H. Exploring complex networks[J]. Nature,2001,410(6825): 268-276.
[18]	HONEYCUTT R L. Stochastic Runge-Kutta algorithms, Ⅰ: white noise[J]. Physical Review A,1992,45(2): 600-603.