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

Weifang HUANG; Lijian YANG; Xuan ZHAN; Ziying FU; Ya JIA

doi:10.1631/FITEE.2300008

Your Location：

Home >

Browse articles >

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

Regular Papers | Updated：2023-10-25

- Synchronization transition of a modular neural network containing subnetworks of different scales
- 包含不同尺度子网络的模块化神经网络同步转换
- Frontiers of Information Technology & Electronic Engineering Vol. 24, Issue 10, Pages: 1458-1470(2023)
- Affiliations：
  
  1.College of Physics Science and Technology, Central China Normal University, Wuhan 430079, China
  2.School of Life Sciences, Central China Normal University, Wuhan 430079, China
- Author bio：
  
  ‡Corresponding author
- Funds：
- DOI：10.1631/FITEE.2300008
  CLC： TN95
- Received：04 January 2023，
  
  Revised：2023-03-05，
  
  Published：0 October 2023
- Accepted：
Scan QR Code
Weifang HUANG, Lijian YANG, Xuan ZHAN, et al. Synchronization transition of a modular neural network containing subnetworks of different scales[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(10): 1458-1470.
DOI：

Weifang HUANG, Lijian YANG, Xuan ZHAN, et al. Synchronization transition of a modular neural network containing subnetworks of different scales[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(10): 1458-1470. DOI： 10.1631/FITEE.2300008.

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。

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.

关键词

Keywords

references

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 https://doi.‍org/10.1103/PhysRevE.100.022224

Andreev AV , Maksimenko VA , Pisarchik AN , et al. , 2021 . Synchronization of interacted spiking neuronal networks with inhibitory coupling . Chaos Sol Fract , 146 : 110812 . https://doi.org/10.1016/j.chaos.2021.110812 https://doi.org/10.1016/j.chaos.2021.110812

Barabási AL , Albert R , 1999 . Emergence of scaling in random networks . Science , 286 ( 5439 ): 509 - 512 . https://doi.org/10.1126/science.286.5439.509 https://doi.org/10.1126/science.286.5439.509

Bard Ermentrout G , Terman DH , 2010 . Mathematical Foundations of Neuroscience . Springer , New York, USA . https://doi.org/10.1007/978-0-387-87708-2 https://doi.org/10.1007/978-0-387-87708-2

Bassett DS , Bullmore E , 2006 . Small-world brain networks . Neuroscientist , 12 ( 6 ): 512 - 523 . https://doi.org/10.1177/1073858406293182 https://doi.org/10.1177/1073858406293182

Bullmore E , Sporns O , 2009 . Complex brain networks: graph theoretical analysis of structural and functional systems . Nat Rev Neurosci , 10 ( 3 ): 186 - 198 . https://doi.org/10.1038/nrn2575 https://doi.org/10.1038/nrn2575

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 . https://doi.org/10.1093/brain/awv051 https://doi.org/10.1093/brain/awv051

Dhamala M , Jirsa VK , Ding MZ , 2004 . Enhancement of neural synchrony by time delay . Phys Rev Lett , 92 ( 7 ): 074104 . https://doi.org/10.1103/physrevlett.92.074104 https://doi.org/10.1103/physrevlett.92.074104

Eguíluz VM , Chialvo DR , Cecchi GA , et al. , 2005 . Scale-free brain functional networks . Phys Rev Lett , 94 ( 1 ): 018102 . https://doi.org/10.1103/PhysRevLett.94.018102 https://doi.org/10.1103/PhysRevLett.94.018102

Fell J , Axmacher N , 2011 . The role of phase synchronization in memory processes . Nat Rev Neurosci , 12 ( 2 ): 105 - 118 . https://doi.org/10.1038/nrn2979 https://doi.org/10.1038/nrn2979

FitzHugh R , 1961 . Impulses and physiological states in theoretical models of nerve membrane . Biophys J , 1 ( 6 ):‍ 445 - 466 . https://doi.org/10.1016/S0006-3495(61)86902-6 https://doi.org/10.1016/S0006-3495(61)86902-6

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 . https://doi.org/10.1523/JNEUROSCI.22-09-03739.2002 https://doi.org/10.1523/JNEUROSCI.22-09-03739.2002

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 . https://doi.org/10.1140/epjst/e2019-900077-7 https://doi.org/10.1140/epjst/e2019-900077-7

Galvan A , Wichmann T , 2008 . Pathophysiology of parkinsonism . Clin Neurophysiol , 119 ( 7 ): 1459 - 1474 . https://doi.org/10.1016/j.clinph.2008.03.017 https://doi.org/10.1016/j.clinph.2008.03.017

Gollo LL , Mirasso C , Sporns O , et al. , 2014 . Mechanisms of zero-lag synchronization in cortical motifs . PLoS Comput Biol , 10 ( 4 ): e1003548 . https://doi.org/10.1371/journal.pcbi.1003548 https://doi.org/10.1371/journal.pcbi.1003548

Gonze D , Bernard S , Waltermann C , et al. , 2005 . Spontaneous synchronization of coupled circadian oscillators . Biophys J , 89 ( 1 ): 120 - 129 . https://doi.org/10.1529/biophysj.104.058388 https://doi.org/10.1529/biophysj.104.058388

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 . https://doi.org/10.1016/j.physa.2011.12.027 https://doi.org/10.1016/j.physa.2011.12.027

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 . https://doi.org/10.1073/pnas.0135058100 https://doi.org/10.1073/pnas.0135058100

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 . https://doi.org/10.1007/s11571-020-09622-5 https://doi.org/10.1007/s11571-020-09622-5

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 . https://doi.org/10.3934/era.2021035 https://doi.org/10.3934/era.2021035

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 . https://doi.org/10.1103/PhysRevE.85.061905 https://doi.org/10.1103/PhysRevE.85.061905

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 . https://doi.org/10.1063/1.5037207 https://doi.org/10.1063/1.5037207

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 . https://doi.org/10.1155/2020/8823111 https://doi.org/10.1155/2020/8823111

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 . https://doi.org/10.1631/FITEE.1900456 https://doi.org/10.1631/FITEE.1900456

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 . https://doi.org/10.1007/s11071-021-06907-0 https://doi.org/10.1007/s11071-021-06907-0

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 . https://doi.org/10.1073/pnas.1705965114 https://doi.org/10.1073/pnas.1705965114

Hilgetag CC , Kaiser M , 2004 . Clustered organization of cortical connectivity . Neuroinformatics , 2 ( 3 ): 353 - 360 . https://doi.org/10.1385/NI:2:3:353 https://doi.org/10.1385/NI:2:3:353

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 . https://doi.org/10.1098/rspb.1984.0024 https://doi.org/10.1098/rspb.1984.0024

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 . https://doi.org/10.1113/jphysiol.1952.sp004764 https://doi.org/10.1113/jphysiol.1952.sp004764

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 . https://doi.org/10.3389/fncom.2018.00059 https://doi.org/10.3389/fncom.2018.00059

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 . https://doi.org/10.1142/S0218127419501566 https://doi.org/10.1142/S0218127419501566

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 . https://doi.org/10.1007/s11071-022-07298-6 https://doi.org/10.1007/s11071-022-07298-6

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 . https://doi.org/10.3389/fncom.2022.791189 https://doi.org/10.3389/fncom.2022.791189

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 . https://doi.org/10.1155/2017/7628537 https://doi.org/10.1155/2017/7628537

Majhi S , Perc M , Ghosh D , 2022 . Dynamics on higher-order networks: a review . J R Soc Interf , 19 ( 188 ):‍ 20220043 . https://doi.org/10.1098/rsif.2022.0043 https://doi.org/10.1098/rsif.2022.0043

Meunier D , Lambiotte R , Bullmore ET , 2010 . Modular and hierarchically modular organization of brain networks . Front Neurosci , 4 : 200 . https://doi.org/10.3389/fnins.2010.00200 https://doi.org/10.3389/fnins.2010.00200

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 . https://doi.org/10.1016/S0167-2789(00)00087-7 https://doi.org/10.1016/S0167-2789(00)00087-7

Morris C , Lecar H , 1981 . Voltage oscillations in the barnacle giant muscle fiber . Biophys J , 35 ( 1 ): 193 - 213 . https://doi.org/10.1016/S0006-3495(81)84782-0 https://doi.org/10.1016/S0006-3495(81)84782-0

Nagumo J , Sato S , 1972 . On a response characteristic of a mathematical neuron model . Kybernetik , 10 ( 3 ): 155 - 164 . https://doi.org/10.1007/BF00290514 https://doi.org/10.1007/BF00290514

Parastesh F , Jafari S , Azarnoush H , et al. , 2021 . Chimeras . Phys Rep , 898 : 1 - 114 . https://doi.org/10.1016/j.physrep.2020.10.003 https://doi.org/10.1016/j.physrep.2020.10.003

Parastesh F , Rajagopal K , Jafari S , et al. , 2022 . Blinking coupling enhances network synchronization . Phys Rev E , 105 ( 5 ): 054304 . https://doi.org/10.1103/PhysRevE.105.054304 https://doi.org/10.1103/PhysRevE.105.054304

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 . https://doi.org/10.1038/s41598-019-54577-1 https://doi.org/10.1038/s41598-019-54577-1

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 . https://doi.org/10.1371/journal.pcbi.1004100 https://doi.org/10.1371/journal.pcbi.1004100

Rodriguez E , George N , Lachaux JP , et al. , 1999 . Perception's shadow: long-distance synchronization of human brain activity . Nature , 397 ( 6718 ): 430 - 433 . https://doi.org/10.1038/17120 https://doi.org/10.1038/17120

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 . https://doi.org/10.1038/385157a0 https://doi.org/10.1038/385157a0

Singer W , 1993 . Synchronization of cortical activity and its putative role in information processing and learning . Ann Rev Physiol , 55 : 349 - 374 . https://doi.org/10.1146/annurev.ph.55.030193.002025 https://doi.org/10.1146/annurev.ph.55.030193.002025

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 . https://doi.org/10.1007/s11071-017-3600-4 https://doi.org/10.1007/s11071-017-3600-4

Sun XJ , Lei JZ , Perc M , et al. , 2011 . Burst synchronization transitions in a neuronal network of subnetworks . Chaos , 21 ( 1 ): 016110 . https://doi.org/10.1063/1.3559136 https://doi.org/10.1063/1.3559136

Uhlhaas PJ , Pipa G , Lima B , et al. , 2009 . Neural synchrony in cortical networks: history, concept and current status . Front Integr Neurosci , 3 : 17 . https://doi.org/10.3389/neuro.07.017.2009 https://doi.org/10.3389/neuro.07.017.2009

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 . https://doi.org/10.1016/j.euroneuro.2010.03.008 https://doi.org/10.1016/j.euroneuro.2010.03.008

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 . https://doi.org/10.1016/j.neuroimage.2008.08.010 https://doi.org/10.1016/j.neuroimage.2008.08.010

Wainrib G , Touboul J , 2013 . Topological and dynamical complexity of random neural networks . Phys Rev Lett , 110 ( 11 ): 118101 . https://doi.org/10.1103/PhysRevLett.110.118101 https://doi.org/10.1103/PhysRevLett.110.118101

Wang GP , Jin WY , Wang A , 2015 . Synchronous firing patterns and transitions in small-world neuronal network . Nonl Dynam , 81 ( 3 ): 1453 - 1458 . https://doi.org/10.1007/s11071-015-2080-7 https://doi.org/10.1007/s11071-015-2080-7

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 . https://doi.org/10.1016/j.physa.2022.127274 https://doi.org/10.1016/j.physa.2022.127274

Wang HT , Chen Y , 2016 . Spatiotemporal activities of neural network exposed to external electric fields . Nonl Dynam , 85 ( 2 ): 881 - 891 . https://doi.org/10.1007/s11071-016-2730-4 https://doi.org/10.1007/s11071-016-2730-4

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 . https://doi.org/10.1016/j.physa.2010.03.031 https://doi.org/10.1016/j.physa.2010.03.031

Watts DJ , Strogatz SH , 1998 . Collective dynamics of 'small-world' networks . Nature , 393 ( 6684 ): 440 - 442 . https://doi.org/10.1038/30918 https://doi.org/10.1038/30918

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 . https://doi.org/10.1007/s11071-022-07967-6 https://doi.org/10.1007/s11071-022-07967-6

Xie Y , Yao Z , Ma J , 2022 . Phase synchronization and energy balance between neurons . Front Inform Technol Electron Eng , 23 ( 9 ): 1407 - 1420 . https://doi.org/10.1631/FITEE.2100563 https://doi.org/10.1631/FITEE.2100563

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 . https://doi.org/10.1016/j.neucom.2017.12.036 https://doi.org/10.1016/j.neucom.2017.12.036

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 . https://doi.org/10.1631/FITEE.1800499 https://doi.org/10.1631/FITEE.1800499

Yan B , Parastesh F , He SB , et al. , 2022 . Interlayer and intralayer synchronization in multiplex fractional-order neuronal networks . Fractals , 30 ( 10 ): 2240194 . https://doi.org/10.1142/S0218348X22401946 https://doi.org/10.1142/S0218348X22401946

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 . https://doi.org/10.1007/s11071-019-05246-5 https://doi.org/10.1007/s11071-019-05246-5

Yao CG , He ZW , Nakano T , et al. , 2019 . Inhibitory-autapse-enhanced signal transmission in neural networks . Nonl Dynam , 97 ( 2 ): 1425 - 1437 . https://doi.org/10.1007/s11071-019-05060-z https://doi.org/10.1007/s11071-019-05060-z

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 . https://doi.org/10.1016/j.chaos.2022.111929 https://doi.org/10.1016/j.chaos.2022.111929

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 . https://doi.org/10.1016/j.physa.2022.128330 https://doi.org/10.1016/j.physa.2022.128330

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 . https://doi.org/10.1016/j.cnsns.2022.106894 https://doi.org/10.1016/j.cnsns.2022.106894

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 . https://doi.org/10.1063/1.3620401 https://doi.org/10.1063/1.3620401

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 . https://doi.org/10.1016/j.physa.2013.06.052 https://doi.org/10.1016/j.physa.2013.06.052

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 . https://doi.org/10.1007/s11571-014-9310-4 https://doi.org/10.1007/s11571-014-9310-4

Yu S , Huang DB , Singer W , et al. , 2008 . A small world of neuronal synchrony . Cereb Cort , 18 ( 12 ): 2891 - 2901 . https://doi.org/10.1093/cercor/bhn047 https://doi.org/10.1093/cercor/bhn047

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 . https://doi.org/10.1142/S0218127422300038 https://doi.org/10.1142/S0218127422300038

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 . https://doi.org/10.1007/s11431-021-2042-4 https://doi.org/10.1007/s11431-021-2042-4

Zhang XY , Li CD , Li HF , et al. , 2022 . Delayed distributed impulsive synchronization of coupled neural networks with mixed couplings . Neurocomputing , 507 : 117 - 129 . https://doi.org/10.1016/j.neucom.2022.07.045 https://doi.org/10.1016/j.neucom.2022.07.045

Views

113

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits

Networking and communication challenges for post-exascale systems

A keyed-hashing based self-synchronization mechanism for port address hopping communication

A multipurpose audio watermarking algorithm with synchronization and encryption

Blinking adaptation for synchronizing a mobile agent network

Related Author

Zhao YAO

Aatef HOBINY

Jun MA

Yu-meng XU

Dhabaleswar PANDA

Xiao-yi LU

Hari SUBRAMONI

Xiao-feng WANG

Related Institution

Department of Physics, Lanzhou University of Technology

NAAM-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Department of Computer Science and Engineering, The Ohio State University

College of Computer, National University of Defense Technology

School of Electrical and Electronic Engineering, Nanyang Technological University

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰