Volume 43 Issue 1
Jan.  2013
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WANG Qingyun, ZHUANG Honghui. ADVANCES OF SYNHRONIZATION TRANSITION IN NUERONAL NETWORKS[J]. Advances in Mechanics, 2013, 43(1): 149-162. doi: 10.6052/1000-0992-12-023
Citation: WANG Qingyun, ZHUANG Honghui. ADVANCES OF SYNHRONIZATION TRANSITION IN NUERONAL NETWORKS[J]. Advances in Mechanics, 2013, 43(1): 149-162. doi: 10.6052/1000-0992-12-023

ADVANCES OF SYNHRONIZATION TRANSITION IN NUERONAL NETWORKS

doi: 10.6052/1000-0992-12-023
Funds:  The project was supported by the National Natural Science Foundation of China (11172017).
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  • Corresponding author: WANG Qingyun
  • Received Date: 2012-02-28
  • Rev Recd Date: 2012-02-28
  • Publish Date: 2013-01-24
  • There exist rich synchronization modes in biological neuronal systems, and conditions to realize different synchronizations have been investigated extensively. However, it is difficult to study the transitions among different synchronizations, though many efforts have been made. This paper mainly focuses on recent advances of synchronization transitions in neuronal systems. Complicated synchronization transitions and its possible mechanism are uncovered when the neuronal systems are subjected to different conditions such as coupling, delay and network topology. Finally, conclusion is drawn and some outlooks of future research are suggested.

     

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  • 1 Gray C M, Konig P, Engel A K, et al. Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature, 1989, 338: 334-337  
    2 Steinmeta P N, Roy A, Fitzgerald P J, et al. Attention modulates synchronized neuronal firing in primate somatosensory cortex. Nature, 2000, 404: 187-190  
    3 Fell J, Fernandez G, Klaver P, et al. Is synchronized neuronal gamma activity relevant for selective attentions. Brain Research Reviews, 2003, 42: 265-272  
    4 Bahar S, Moss F. Stochastic resonance and synchronization in the crayfish caudal photoreceptor. Biosciences,2004, 188: 81-97  
    5 Terman D, Kopell N, Bose A. Dynamics of two mutually coupled slow inhibitory neurons. Physica D, 1998, 117(1):241-275  
    6 Rubin J, Terman D. Geometric analysis of neuronal firing patterns in network models with fast inhibitory synapses. Neurocomputing, 1999, 26-27: 491-498
    7 Terman D, Ahn S, Wang X Y, et al. Reducing neuronal networks to discrete dynamics. Physica D, 2008, 237: 324-338  
    8 Yoshioka M. Cluster synchronization in an ensemble of neurons interacting through chemical synapses. Phys. Rev. E, 2005, 71: 061914  
    9 Shi X, Lu Q S. Complete synchronization of coupled Hindmarsh-Rose neurons with ring structure. Chin. Phys. Lett., 2004, 21: 1695-1698  
    10 Wang Q Y, Lu Q S, Chen G R, et al. Chaos synchronization of coupled neurons with gap junctions. Phys. Lett. A, 2006, 356: 17-25  
    11 Wang Q Y, Duan Z S, Huang L, et al. Pattern formation and firing synchronization in networks of map neurons. New J. Phys, 2007, 9(383): 1-11
    12 Belykh I, de Lange E, Hasler M. Synchronization of bursting neurons: What matters in the network topology. Phys. Rev. Lett., 2005, 94:188101  
    13 Kopell N, Ermentrout B. Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks. Proc. Natl. Acad. Sci. USA,2004, 101: 15482-15487  
    14 Kwon O, Moon H T. Coherence resonance in small-world networks of excitable cells. Phys. Lett. A, 2002, 298:319-324  
    15 Wang Q Y, Duan Z S, Perc M, et al. Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability. Europhys. Lett., 2008, 83: 50008  
    16 Tanakaa G, Ibarz B, Sanjuan MAF, et al. Synchronization and propagation of bursts in networks of coupled map neurons. Chaos, 2006, 16: 013113  
    17 Zhou C S, Zemanov L, Zamora G, et al. Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett., 2006, 97: 238103  
    18 Leyva I, Sendi?na-Nadal I, Almendral JA, et al. Sparse repulsive coupling enhances synchronization in complex networks. Phys Rev E, 2006, 74: 056112  
    19 Wang R B, Zhang Z K. Phase synchronization motion and neural coding in dynamic transmission of neural information. IEEE Transactions on Neural Networks, 2011,22(7): 1097-1106  
    20 Wang R B, Zhang Z K, Tee C K. Neurodynamics analysis on transmission of brain information. Applied Mathematics and Mechanics, 2009, 30(11): 1415-1428  
    21 Wang R B, Jiao X F. A stochastic nonlinear evolution model and neural coding on neuronal population possessing variable coupling intensity in spontaneous behavior. Neurocomputing, 2006, (7-9): 778-785
    22 陆启韶, 刘深泉, 刘锋, 等. 生物神经网络系统动力学与功能 研究. 力学进展, 2008, 38(6): 766-793.
    23 Dhamala M, Jirsa V K, Ding M Z. Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett.,2004, 92 : 02810
    24 Wang Q Y, Duan Z S, Feng Z S, et al. Synchronization transition in gap-junction-coupled leech neurons. Physica A, 2008, 387 (16-17): 4404-4410
    25 Wang Q Y, Lu Q S, Chen G R. Ordered bursting synchronization and complex wave propagation in a ring neuronal network. Physica A, 2007, 374: 869-878  
    26 Shen Y, Hou Z H, Xin H W. Transition to burst synchronization in coupled neuron networks. Phys Rev E, 2008,77: 031920  
    27 Sun X J, Lei J Z, Perc M, et al. Burst synchronization transitions in a neuronal network of subnetworks. Chaos,2011, 21: 016110  
    28 Dhamala M, Jirsa V K, Ding M Z. Enhancement of neural synchrony by time delay. Phys. Rev. Lett., 2004, 92:074104  
    29 Wang Q Y, Lu Q S. Time-delay enhanced synchronization and regularization in two coupled chaotic ML neurons. Chin. Phys. Lett., 2005, 22: 543-546  
    30 Wang Q Y, Lu Q S, Chen G R. Synchronization transition induced by synaptic delay in coupled fast spiking neurons. International Journal of Bifurcation and Chaos, 2008,18(4): 1189-1198  
    31 Wang Q Y, Chen G R, Perc M. Synchronous bursts on scale-Free neuronal networks with attractive and repulsive coupling. PLoS ONE, 2011, 6(1): e15851  
    32 Wang Q Y, Chen G R. Delay-induced intermittent transition of synchronization in neuronal networks with hybrid synapses. Chaos, 2011, 21(1): 013123  
    33 Wang Q Y, Lu Q S, Chen G R, et al. Bifurcation and synchronization of synaptically coupled FHN models with time delay. Chaos, Solitons & Fractals, 2009, 39(2): 918-925  
    34 Adhikari B M, Prasad A. Time-delay-induced phasetransition to synchrony in coupled bursting neurons. Chaos, 2011, 21: 023116  
    35 Mancilla J G, Lewis T J, Pinto D J, et al. Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex. J Neurosci, 2007, 27: 2058-2073  
    36 Gibson J R, Beierlein M, Connors B W. Two networks of electrically coupled inhibitory neurons in neocortex. Journal of Computational Neuroscience, 2005, 18: 287-295  
    37 Gao J, Holmes P. On the dynamics of electrically-coupled neurons with inhibitory synapses. Journal of Computational Neuroscience, 2007, 22: 39-61  
    38 Verheijck E E, Wilders R, Joyner R W, et al. Pacemaker synchronization of electrically coupled rabbit sinoatrial node cells. J Gen Physiol., 1998, 111(1): 95-112  
    39 Audesirk G, Audesirk T, Bowsher P. Variability and frequent failure of Lucifer yellow to pass between two electrically coupled neurons in Lymnaea stagnalis. Journal of Neurobiology, 1982, 13(4): 369-375  
    40 Venance L, Rozov A. Connexin expression in electrically coupled postnatal rat brain neurons. PNAS, 2000, 97 (18): 10261-10265
    41 Wang Q Y, Lu Q S, Wang H X. Transition to complete synchronization via near-synchronization in two coupled chaotic neurons. Chinese Physics, 2005, 14: 2189-2195  
    42 Balenzuela P, García-Ojalvo J. Role of chemical synapses in coupled neurons with noise. Physical Review E, 2005,72: 021901  
    43 Lang M, Marquez-Lago TT, Stelling J, et al. Autonomous synchronization of chemically coupled synthetic oscillators. Bull Math Biol, 2011, 73(11): 2678-706  
    44 Franovic I, Miljkovic V. Power law behavior related to mutual synchronization of chemically coupled map neurons. Eur. Phys. J. B, 2010, 76: 613-624  
    45 Shi X, Lu Q S. Burst synchronization of electrically and chemically coupled map-based neurons. Physica A, 2009,388: 2410-2419  
    46 Lysetskiy M, Zurada J M. Bifurcating neuron: Computation and learning. Neural Networks, 2004, 17: 225-232  
    47 Wang Q Y, Sanjuan Miguel AF, Chen G R. Transition of phase locking modes in a minimal neuronal network. Neurocomputing, 2012, 81: 60-66  
    48 Sato Y D, Okumura K, Ichiki A, et al. Temperaturemodulated synchronization transition in coupled neuronal oscillators. Physical Review E, 2012, 85: 031910  
    49 Yin H B, Cox C L, Mehta P G, et al. Bifurcation analysis of a thalamic relay neuron model. In: Proc. American Control Conference, St. Louis, MO, USA, 2009
    50 Tsumoto K, Yoshinaga T, Kawakami H. Bifurcations of synchronized responses in synaptically coupled Bonhoffervan der Pol neurons. Physical Review E, 2002, 65: 036230  
    51 Wang H X, Lu Q S, Wang Q Y. Bursting and synchronization transition in the coupled modified ML neurons. Communications in Nonlinear Science and Numerical Simulation, 2008, 13: 1668-1675  
    52 Postnova S, Voigt K, Braun H A. Neural synchronization at tonic-to-bursting transitions. J Biol Phys, 2007,33:129-143  
    53 Yu H, Wang J, Liu Q, et al. Chaotic phase synchronization in a modular neuronal network of small-world subnetworks. Chaos, 2011, 21(4): 043125  
    54 Yassin L, Benedetti Brett L. An embedded subnetwork of highly active neurons in the neocortex. Neuron, 2010, 68:1043-1050  
    55 Tang J, Ma J, Yi M, et al. Delay and diversity-induced synchronization transitions in a small-world neuronal network. Physical Review E, 2011, 83: 046207  
    56 Wang Q Y, Aleksandra M, Perc M, et al. Taming desynchronized bursting with delays in the Macaque cortical network. Chin. Phys. B, 2011, 20 (4): 040504  
    57 Cui J, Canavier C C, Butera R J. Functional phase response curves: A method for understanding synchronization of adapting neurons. Journal of Neurophysiology, 2009, 102(1), 387-398  
    58 Galan R F, Ermentrout, G B, Urban N N. Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. Physical Review Letters, 2005, 94(15), 158101  
    59 Galan R F, Bard Ermentrout G, Urban N N. Predicting synchronized neural assemblies from experimentally estimated phase-resetting curves. Neurocomputing, 2006,69(10-12): 1112-1115
    60 Winfree A T. The Geometry of Biological Time. New York: Springer Verlag, 1980, 530
    61 Canavier C C, Gurel Kazanci F, Prinz A A. Phase resetting curves allow for simple and accurate prediction of robust N:1 phase locking for strongly coupled neural oscillators. Biophys. J., 2009, 97: 59-73  
    62 Canavier C C. The application of phase resetting curves to the analysis of pattern generating circuits containing bursting neurons. In: Coombes S, Bressloff P, eds. Bursting: The Genesis of Rhythm in the Nervous System. Singapore: World Scienti c, 2005. 175-200
    63 Smeal R M, Ermentrout G B, White J A. Phase-response curves and synchronized neural networks. Philosophical Transactions of the Royal Society B-Biological Sciences,2010, 365(1551): 2407-2422  
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