Full Text:   <1605>

Summary:  <218>

Suppl. Mater.: 

CLC number: TN95

On-line Access: 2023-10-27

Received: 2023-01-04

Revision Accepted: 2023-03-05

Crosschecked: 2023-10-27

Cited: 0

Clicked: 485

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Ya JIA

https://orcid.org/0000-0002-2818-9074

Weifang HUANG

https://orcid.org/0009-0006-8404-8109

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2023 Vol.24 No.10 P.1458-1470

http://doi.org/10.1631/FITEE.2300008


Synchronization transition of a modular neural network containing subnetworks of different scales


Author(s):  Weifang HUANG, Lijian YANG, Xuan ZHAN, Ziying FU, Ya JIA

Affiliation(s):  College of Physics Science and Technology, Central China Normal University, Wuhan 430079, China; more

Corresponding email(s):   jiay@ccnu.edu.cn

Key Words:  Hodgkin–, Huxley neuron, Modular neural network, Subnetwork, Synchronization, Transmission delay


Weifang HUANG, Lijian YANG, Xuan ZHAN, Ziying FU, Ya JIA. Synchronization transition of a modular neural network containing subnetworks of different scales[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(10): 1458-1470.

@article{title="Synchronization transition of a modular neural network containing subnetworks of different scales",
author="Weifang HUANG, Lijian YANG, Xuan ZHAN, Ziying FU, Ya JIA",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="24",
number="10",
pages="1458-1470",
year="2023",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2300008"
}

%0 Journal Article
%T Synchronization transition of a modular neural network containing subnetworks of different scales
%A Weifang HUANG
%A Lijian YANG
%A Xuan ZHAN
%A Ziying FU
%A Ya JIA
%J Frontiers of Information Technology & Electronic Engineering
%V 24
%N 10
%P 1458-1470
%@ 2095-9184
%D 2023
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2300008

TY - JOUR
T1 - Synchronization transition of a modular neural network containing subnetworks of different scales
A1 - Weifang HUANG
A1 - Lijian YANG
A1 - Xuan ZHAN
A1 - Ziying FU
A1 - Ya JIA
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 24
IS - 10
SP - 1458
EP - 1470
%@ 2095-9184
Y1 - 2023
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2300008


Abstract: 
Time delay and coupling strength are important factors that affect the synchronization of neural networks. In this study, a modular neural network containing subnetworks of different scales was constructed using the hodgkin–;Huxley (HH) neural model; i.‍e., a small-scale random network was unidirectionally connected to a large-scale small-world network through chemical synapses. Time delays were found to induce multiple synchronization transitions in the network. An increase in coupling strength also promoted synchronization of the network when the time delay was an integer multiple of the firing period of a single neuron. Considering that time delays at different locations in a modular network may have different effects, we explored the influence of time delays within each subnetwork and between two subnetworks on the synchronization of modular networks. We found that when the subnetworks were well synchronized internally, an increase in the time delay within both subnetworks induced multiple synchronization transitions of their own. In addition, the synchronization state of the small-scale network affected the synchronization of the large-scale network. It was surprising to find that an increase in the time delay between the two subnetworks caused the synchronization factor of the modular network to vary periodically, but it had essentially no effect on the synchronization within the receiving subnetwork. By analyzing the phase difference between the two subnetworks, we found that the mechanism of the periodic variation of the synchronization factor of the modular network was the periodic variation of the phase difference. Finally, the generality of the results was demonstrated by investigating modular networks at different scales.

包含不同尺度子网络的模块化神经网络同步转换

黄卫芳1,杨利建1,詹璇1,付子英2,贾亚1
1华中师范大学物理科学与技术学院,中国武汉市,430079
2华中师范大学生命科学学院,中国武汉市,430079
摘要:时间延迟和耦合强度是影响神经网络同步的重要因素。本文利用霍奇金-赫胥黎(HH)神经元模型构建一个包含不同尺度子网络的模块化神经网络,即小尺度随机网络通过化学突触与大尺度小世界网络单向连接。研究发现,时间延迟在网络中诱发了多个同步转换。当时间延迟是单个神经元放电周期的整数倍时,耦合强度增加也促进网络同步化。考虑到模块化网络中不同位置的时间延迟可能具有不同作用,我们探讨子网络之间以及子网络内部的时间延迟对模块化网络同步的影响。我们发现,当子网络内同步良好时,两个子网络内部时间延迟增加会诱发其自身出现多个同步转换。此外,小尺度网络的同步状态会影响大尺度网络的同步。进一步发现,两个子网络之间的时间延迟诱导模块化网络的同步转换,但对接收信号的子网络内的同步基本无影响。通过分析两个子网络之间的相位差,我们发现模块化网络出现同步转换的机制是相位差的周期性变化。最后,通过对不同尺度模块化网络的研究,证明了本文结果的泛化性。

关键词:霍奇金-赫胥黎神经元;模块化神经网络;子网络;同步;时间延迟

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Andreev AV, Frolov NS, Pisarchik AN, et al., 2019. Chimera state in complex networks of bistable Hodgkin-Huxley neurons. Phys Rev E, 100(2):022224. https://doi.‍org/10.1103/PhysRevE.100.022224

[2]Andreev AV, Maksimenko VA, Pisarchik AN, et al., 2021. Synchronization of interacted spiking neuronal networks with inhibitory coupling. Chaos Sol Fract, 146:110812.

[3]Barabási AL, Albert R, 1999. Emergence of scaling in random networks. Science, 286(5439):509-512.

[4]Bard Ermentrout G, Terman DH, 2010. Mathematical Foundations of Neuroscience. Springer, New York, USA.

[5]Bassett DS, Bullmore E, 2006. Small-world brain networks. Neuroscientist, 12(6):512-523.

[6]Bullmore E, Sporns O, 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci, 10(3):186-198.

[7]Cheng W, Rolls ET, Gu HG, et al., 2015. Autism: reduced connectivity between cortical areas involved in face expression, theory of mind, and the sense of self. Brain, 138(5):1382-1393.

[8]Dhamala M, Jirsa VK, Ding MZ, 2004. Enhancement of neural synchrony by time delay. Phys Rev Lett, 92(7):074104.

[9]Eguíluz VM, Chialvo DR, Cecchi GA, et al., 2005. Scale-free brain functional networks. Phys Rev Lett, 94(1):018102.

[10]Fell J, Axmacher N, 2011. The role of phase synchronization in memory processes. Nat Rev Neurosci, 12(2):105-118.

[11]FitzHugh R, 1961. Impulses and physiological states in theoretical models of nerve membrane. Biophys J, 1(6):‍445-466.

[12]Fries P, Schröeder JH, Roelfsema PR, et al., 2002. Oscillatory neuronal synchronization in primary visual cortex as a correlate of stimulus selection. J Neurosci, 22(9):‍3739-3754.

[13]Frolov NS, Maksimenko VA, Khramova MV, et al., 2019. Dynamics of functional connectivity in multilayer cortical brain network during sensory information processing. Eur Phys J Spec Top, 228(11):2381-2389.

[14]Galvan A, Wichmann T, 2008. Pathophysiology of parkinsonism. Clin Neurophysiol, 119(7):1459-1474.

[15]Gollo LL, Mirasso C, Sporns O, et al., 2014. Mechanisms of zero-lag synchronization in cortical motifs. PLoS Comput Biol, 10(4):e1003548.

[16]Gonze D, Bernard S, Waltermann C, et al., 2005. Spontaneous synchronization of coupled circadian oscillators. Biophys J, 89(1):120-129.

[17]Gosak M, Markovič R, Marhl M, 2012. The role of neural architecture and the speed of signal propagation in the process of synchronization of bursting neurons. Phys A Stat Mech Appl, 391(8):2764-2770.

[18]Greicius MD, Krasnow B, Reiss AL, et al., 2003. Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proc Nat Acad Sci USA, 100(1):253-258.

[19]Gu XC, Han F, Wang ZJ, 2021a. Dependency analysis of frequency and strength of gamma oscillations on input difference between excitatory and inhibitory neurons. Cogn Neurodynam, 15(3):501-515.

[20]Gu XC, Han F, Wang ZJ, et al., 2021b. Enhancement of gamma oscillations in E/I neural networks by increase of difference between external inputs. Electron Res Arch, 29(5):3227-3241.

[21]Guo DQ, Wang QY, Perc M, 2012. Complex synchronous behavior in interneuronal networks with delayed inhibitory and fast electrical synapses. Phys Rev E, 85(6):061905.

[22]Han F, Gu XC, Wang ZJ, et al., 2018. Global firing rate contrast enhancement in E/I neuronal networks by recurrent synchronized inhibition. Chaos, 28(10):106324.

[23]Han F, Wang ZJ, Fan H, et al., 2020. High-frequency synchronization improves firing rate contrast and information transmission efficiency in E/I neuronal networks. Neur Plast, 2020:8823111.

[24]Han XP, Zhao YS, Li XD, 2020. A survey on complex dynamical networks with impulsive effects. Front Inform Technol Electron Eng, 21(2):199-219.

[25]He ZW, Yao CG, Liu S, et al., 2021. Transmission of pacemaker signal in a small world neuronal networks: temperature effects. Nonl Dynam, 106(3):2547-2557.

[26]Helfrich RF, Huang M, Wilson G, et al., 2017. Prefrontal cortex modulates posterior alpha oscillations during top-down guided visual perception. Proc Nat Acad Sci USA, 114(35):9457-9462.

[27]Hilgetag CC, Kaiser M, 2004. Clustered organization of cortical connectivity. Neuroinformatics, 2(3):353-360.

[28]Hindmarsh JL, Rose RM, 1984. A model of neuronal bursting using three coupled first order differential equations. Proc R Soc B Biol Sci, 221(1222):87-102.

[29]Hodgkin AL, Huxley AF, 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 117(4):500-544.

[30]Khoshkhou M, Montakhab A, 2018. Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type. Front Comput Neurosci, 12:59.

[31]Liu Y, Ma J, Xu Y, et al., 2019. Electrical mode transition of hybrid neuronal model induced by external stimulus and electromagnetic induction. Int J Bifurc Chaos, 29(11):1950156.

[32]Liu ZL, Han F, Wang QY, 2022a. A review of computational models for gamma oscillation dynamics: from spiking neurons to neural masses. Nonl Dynam, 108(3):‍‍‍1849-1866.

[33]Liu ZL, Wang QY, Han F, 2022b. Synaptic role in facilitating synchronous theta oscillations in a hybrid hippocampal neuronal network. Front Comput Neurosci, 16:791189.

[34]Lu LL, Jia Y, Liu WH, et al., 2017. Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. Complexity, 2017:7628537.

[35]Majhi S, Perc M, Ghosh D, 2022. Dynamics on higher-order networks: a review. J R Soc Interf, 19(188):‍20220043.

[36]Meunier D, Lambiotte R, Bullmore ET, 2010. Modular and hierarchically modular organization of brain networks. Front Neurosci, 4:200.

[37]Mormann F, Lehnertz K, David P, et al., 2000. Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Phys D Nonl Phenom, 144(3-4):358-369.

[38]Morris C, Lecar H, 1981. Voltage oscillations in the barnacle giant muscle fiber. Biophys J, 35(1):193-213.

[39]Nagumo J, Sato S, 1972. On a response characteristic of a mathematical neuron model. Kybernetik, 10(3):155-164.

[40]Parastesh F, Jafari S, Azarnoush H, et al., 2021. Chimeras. Phys Rep, 898:1-114.

[41]Parastesh F, Rajagopal K, Jafari S, et al., 2022. Blinking coupling enhances network synchronization. Phys Rev E, 105(5):054304.

[42]Pisarchik AN, Maksimenko VA, Andreev AV, et al., 2019. Coherent resonance in the distributed cortical network during sensory information processing. Sci Rep, 9(1):18325.

[43]Ponce-Alvarez A, Deco G, Hagmann P, et al., 2015. Resting-state temporal synchronization networks emerge from connectivity topology and heterogeneity. PLoS Comput Biol, 11(2):e1004100.

[44]Rodriguez E, George N, Lachaux JP, et al., 1999. Perception’s shadow: long-distance synchronization of human brain activity. Nature, 397(6718):430-433.

[45]Roelfsema PR, Engel AK, König P, et al., 1997. Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature, 385(6612):157-161.

[46]Singer W, 1993. Synchronization of cortical activity and its putative role in information processing and learning. Ann Rev Physiol, 55:349-374.

[47]Sun XJ, Li GF, 2017. Synchronization transitions induced by partial time delay in a excitatory‍–‍inhibitory coupled neuronal network. Nonl Dynam, 89(4):2509-2520.

[48]Sun XJ, Lei JZ, Perc M, et al., 2011. Burst synchronization transitions in a neuronal network of subnetworks. Chaos, 21(1):016110.

[49]Uhlhaas PJ, Pipa G, Lima B, et al., 2009. Neural synchrony in cortical networks: history, concept and current status. Front Integr Neurosci, 3:17.

[50]van den Heuvel MP, Pol HEH, 2010. Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur Neuropsychopharm, 20(8):519-534.

[51]van den Heuvel MP, Stam CJ, Boersma M, et al., 2008. Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain. NeuroImage, 43(3):528-539.

[52]Wainrib G, Touboul J, 2013. Topological and dynamical complexity of random neural networks. Phys Rev Lett, 110(11):118101.

[53]Wang GP, Jin WY, Wang A, 2015. Synchronous firing patterns and transitions in small-world neuronal network. Nonl Dynam, 81(3):1453-1458.

[54]Wang GW, Wu Y, Xiao FL, et al., 2022. Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction. Phys A Stat Mech Appl, 598:127274.

[55]Wang HT, Chen Y, 2016. Spatiotemporal activities of neural network exposed to external electric fields. Nonl Dynam, 85(2):881-891.

[56]Wang QY, Perc M, Duan ZS, et al., 2010. Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling. Phys A Stat Mech Appl, 389(16):3299-3306.

[57]Watts DJ, Strogatz SH, 1998. Collective dynamics of 'small-world' networks. Nature, 393(6684):440-442.

[58]Wu Y, Ding QM, Li TY, et al., 2023. Effect of temperature on synchronization of scale-free neuronal network. Nonl Dynam, 111(3):2693-2710.

[59]Xie Y, Yao Z, Ma J, 2022. Phase synchronization and energy balance between neurons. Front Inform Technol Electron Eng, 23(9):1407-1420.

[60]Xu Y, Jia Y, Ge MY, et al., 2018. Effects of ion channel blocks on electrical activity of stochastic Hodgkin‍–‍Huxley neural network under electromagnetic induction. Neurocomputing, 283:196-204.

[61]Xu YM, Yao Z, Hobiny A, et al., 2019. Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits. Front Inform Technol Electron Eng, 20(4):571-583.

[62]Yan B, Parastesh F, He SB, et al., 2022. Interlayer and intralayer synchronization in multiplex fractional-order neuronal networks. Fractals, 30(10):2240194.

[63]Yang XL, Li N, Sun ZK, 2019. Extended analysis of stochastic resonance in a modular neuronal network at different scales. Nonl Dynam, 98(2):1029-1039.

[64]Yao CG, He ZW, Nakano T, et al., 2019. Inhibitory-autapse-enhanced signal transmission in neural networks. Nonl Dynam, 97(2):1425-1437.

[65]Yu D, Wang GW, Ding QM, et al., 2022. Effects of bounded noise and time delay on signal transmission in excitable neural networks. Chaos Sol Fract, 157:111929.

[66]Yu D, Wu Y, Yang LJ, et al., 2023a. Effect of topology on delay-induced multiple resonances in locally driven systems. Phys A Stat Mech Appl, 609:128330.

[67]Yu D, Wang GW, Li TY, et al., 2023b. Filtering properties of Hodgkin-Huxley neuron on different time-scale signals. Commun Nonl Sci Numer Simul, 117:106894.

[68]Yu HT, Wang J, Liu C, et al., 2011. Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker. Chaos, 21(4):047502.

[69]Yu HT, Wang J, Liu C, et al., 2013. Delay-induced synchronization transitions in small-world neuronal networks with hybrid electrical and chemical synapses. Phys A Stat Mech Appl, 392(21):5473-5480.

[70]Yu HT, Wang J, Du JW, et al., 2015. Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses. Cogn Neurodynam, 9(1):93-101.

[71]Yu S, Huang DB, Singer W, et al., 2008. A small world of neuronal synchrony. Cereb Cort, 18(12):2891-2901.

[72]Yuan YY, Han F, Zhu QH, et al., 2022a. Transition of chimera states and synchronization in two-layer networks of coupled hindmarsh-rose neurons. Int J Bifurc Chaos, 32(1):2230003.

[73]Yuan YY, Yang H, Han F, et al., 2022b. Traveling chimera states in locally coupled memristive Hindmarsh-Rose neuronal networks and circuit simulation. Sci China Technol Sci, 65(7):1445-1455.

[74]Zhang XY, Li CD, Li HF, et al., 2022. Delayed distributed impulsive synchronization of coupled neural networks with mixed couplings. Neurocomputing, 507:117-129.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE