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1、02:24:00,1,Some Recent Study in Biological Neuronal Oscillatory Networks,Qingyun Wang(王青云),Department of Dynamics and Control,Beihang University,Beijing 100191,Email:,02:24:00,2,With compliments,Prof.Lu Qishao(Beihang University)Prof.Duan ZhiSheng(Peking University)Prof.Chen GuanRong(City University
2、 of HongKong)Dr.Matjaz Perc(University of Maribor,Koroska cesta 160,SI-2000 Maribor,Slovenia),02:24:00,3,Contents,MotivationNeuronal structure and networkDynamics of a single neuronSynchronization transition and Rhythm dynamics on networksBursting Dynamics on Realistic Neuronal Networks Spatial Reso
3、nance in Neuronal NetworksOpen problems,02:24:00,4,The single neuron in the vertebrate cortex connects to more than 10,000 postsynaptic neurons via synapses forming complex networks.The biological nervous system can communicate and transform information through interaction of networks.Neuronal infor
4、mation encoding and processing are reflected by oscillation patterns of electrical impulse sequences in neurons.,Motivation,02:24:00,5,Neurodynamics deals with the dynamics and control problems of electrical activities and information processes in nervous systems and is important in the research of
5、biological motions and intelligent behavior.Neurodynamics is a multi-disciplinary research area in nonlinear dynamics,network science and neuroscience.Synchronization is of great importance for signal encoding and transduction in information processing of neurons in two respects.Biological neurons c
6、an extract the hindered information by stochastic resonance.,02:24:00,6,6,Neural Medicine and Engineering,Neuronal firing and information encoding,Biological Control,Biological complex neuronal networks,Intelligent Robots,Biological structure of nervous systems,Neural Cognitive Science,Neural Comput
7、ers,Neural Medical Techniques,02:24:00,7,Structure of Single Neuron,A basic element for information processing in nervous systems.There are about 1011 neurons in the human brain and 104 synapses for a neuron.,02:24:00,8,Model of neuron,(1),(4),(3),(2),Hodgkin A.L.,Huxley A.F.,J.physiol.(London),1952
8、,(117)500-544,Hodgkin-Huxley model(1952 Nobel Prize),Chay model,HR model,FHN model,Rulkov map etc.,Nonlinear ODEs involving multiple time scales.Hard to analyze both mathematically and computationally.,02:24:00,9,Diversity of firing patterns of a single neuron(in experimental neural pacemakers)(Li L
9、i,Ren Wei,2003,2004),02:24:00,10,Bifurcation scenario(in theoretical model and experimental neural pacemakers)(Li Li,Ren Wei et al,IJBC,2004.Duan Li Xia et al,Neurocomputing 2008),Chay model,02:24:00,11,Chaos(in experimental neural pacemakers)between period 2 and period 3 firings(Ren Wei,IJBC,1997),
10、02:24:00,12,02:24:00,13,Neuronal networks,What is a Brain?dense networkmore than 104 cell bodies and several kilometers of wires per cubic millimeter.Many types of cells:spiking neurons(1011 cells),glia cells(supporter cells not involved in the information processing)and analog neurons.,02:24:00,14,
11、Synapse and delay,02:24:00,15,Dorsal and lateral views of the connectivity backbone of human brain.Labels indicating anatomical subregions are placed at their respective centers of mass.Nodes(individual ROIs)are coded according to strength and edges are coded according to connection weight.,Hagmann
12、P,Cammoun L,Gigandet X,Meuli R,Honey CJ,Wedeen VJ,Sporns O(2008)Mapping the structural core of human cerebral cortex.PLoS Biology Vol.6,No.7,e159,02:24:00,16,Neuronal networks,Neuronal networks involve a large number of individual neurons.Details of the connectivity not usually known.Hard to analyze
13、 how connectivity influences ODE dynamics.,02:24:00,17,Neuronal synchronization,Synchronization seems to be very crucial for the efficient processing and transmission of information across the nerve system.Parkinsons tremor is related to neuronal synchronization.Transiently synchronized assemblies o
14、f neurons are believed to underlie cognitive functions.There is consistent evidence for a reduction of synchronization in schizophrenia.,02:24:00,18,Robert C.Elson et al,Phys.Review Lett 81 5692-5695 1998,Two coupled neuron circuit,Synchronized motions,02:24:00,19,Hua Guang GU et al,CHIN.PHYS.LETT.V
15、ol.26,No.11(2009)110501,Experiment results,02:24:00,20,PNAS 2010,Listener-speaker can validly communication by means of neuronal coupling,02:24:00,21,Classification of synchronization,02:24:00,22,Burst synchronization and desynchronization in fold/homoclinic(square-wave)bursters.Shown are simulation
16、s of coupled Morris-Lecar systems with additional slow variables.,Various regimes of synchronization of bursters(modied from Izhikevich,2000a).,02:24:00,23,Singular phase locking,02:24:00,24,Analysis method of phase locking,Singular perturbation theory(Terman etal,J Comput Neurosci(2007)23:217235),D
17、ynamic clustering in the(a)full and(b)reduced models.There are twenty pairs of E-and I-cells.Each E-cell excitesone I-cell and each I-cell inhibits three E-cells,Limited:Network structure,connection style,02:24:00,25,Phase response curve(discrete map method),Carmen Canavier,02:24:00,26,There are sti
18、ll many other methods:Hilbert transformation of time series,Poincare map method(numerical computation),02:24:00,27,Incorporating noise and delay,Noise induced(enhanced)synchronization.(two coupled neurons and large scale neuronal networks)Noise induced spatiotemporal wave patterns(target wave,spiral
19、 wave(Ma jun),spatial coherence)Delay induced complexity in neuronal networks(various synchronization transition and spatial coherence),02:24:00,28,Effect of delay on two coupled neurons,Q Y Wang et al,IJBC,18,4(2008)11891198,02:24:00,29,Effect of delay on large scale neuronal networks,Dynamics mode
20、l,02:24:00,30,Zig-zag fronts,Antiphase clustering sunhcronization,In phase synchronization again,02:24:00,31,Measure:,Q.Y.Wang,Z.S Duan,M.Perc,G.R.Chen,EPL,83(2008)50008,02:24:00,32,(Continued),A.-L.Barabsi and R.Albert,Science 286,509 1999,02:24:00,33,Increasing delay,02:24:00,34,02:24:00,35,02:24:
21、00,36,02:24:00,37,02:24:00,38,Qingyun Wang,Matjaz Perc,Zhi Sheng Duan,Guan Rong Chen,Physical Review E,80,026206,2009.,02:24:00,39,Attractive coupling,02:24:00,40,Repulsive coupling,02:24:00,41,Bursting period,02:24:00,42,Bursting synchronization,Macaque cortical network,consisting of 95 nodes and 2
22、402 links,02:24:00,43,Mathematical model,02:24:00,44,Bursting synchronization,Space-time plots of x(t)as obtained for D=2.0 and I_ext=3.2 with different information transmission delays tau,equalling:(a)0,(b)7,(c)14,(d)22,(e)30.Notice the bursting synchronization and spikes in burst increase as tau i
23、ncreases.,Liang Xiao Ming et al,2009 PRE,02:24:00,45,In order to quantitatively describe global network states,we define the quantity m,The more synchronous the neuronal network is,the larger is the parameter m.Further,it can also identify transition of different bursts.Thus,it is called burst synch
24、ronization transition parameter.,02:24:00,46,Dependence of the burst synchronization parameter m on$tau$for different values of diffusion D,02:24:00,47,Dependence of the burst synchronization parameter m on$tau$for different values of the external stimulus I,02:24:00,48,Resonance Resonance of a sing
25、le HH neuron,02:24:00,49,Resonance,02:24:00,50,Spatial resonance of networks,02:24:00,51,Spatial coherence resonance,Model Set-Up,Hodgkin and Huxley model,Transmission delay,noise,the Euler Maruyama method,02:24:00,52,Effect of delay,As the noise increases,pattern is destroyed.,There is an intermedi
26、ate noise,circular pattern can appear.,02:24:00,53,Spatial structure function:,Circular average:,Signal-noise-ratio:,Two dimensional Fourier Transform,02:24:00,54,Spatial structure function,02:24:00,55,Circular average and SNR,Maximum indicating coherence,02:24:00,56,For different delays,dependence
27、of SNR on noise.,02:24:00,57,Effect of small world connection,As q is increased,Snr decreases.,02:24:00,58,Open problems,Dynamical mechanism of synchronization bifurcation:synchronization-antiphase synchronization-synchronization as the delay/link probability is varied on small world/scale free netw
28、orks.Dynamical bifurcation mechanism of bursting firing should be explored as the delay is increased.Theory exploration of singular phase locking.Dynamics of more realistic neuronal networks,02:24:00,59,Q.Y.Wang,Z.S.Duan,L.Huang,G.R.Chen,Q.S.Lu,Pattern formation and firing synchronization in network
29、s of map neurons,New Journal of Physics,9(383):1-11,2007.Q.Y.Wang,Z.S.Duan,Z.S.Feng,G.R.Chen and Q.S.Lu，Synchronization transition in Gap-Junction-Coupled leech neurons,Physica A,2008,387 4404-4410.Q.Y.Wang,Matja Perc,Zhisheng Duan,Guanrong Chen,Delay-enhanced coherence resonance of spiral wave in n
30、oisy Hodgkin-Huxley neuronal networks,Phys.Lett.A,372(2008)5681.Qingyun Wang,Zhisheng Duan,Matja Perc,Guanrong Chen,Synchronization transitions on small-world neuronal networks:effects of information transmission delay and rewiring probability,Europhysics Letters,83(2008)50008Qingyun Wang,Matjaz Per
31、c,Zhi Sheng Duan,Guan Rong Chen,Synchronization transitions on scale-free neuronal networks due to finite information transmission delays,Physical Review E,80,026206,2009.Qingyun Wang,Matjaz Perc,Zhisheng Duan,Guanrong Chen,Delay-induced multiple stochastic resonances on scale-free neuronal networks,Chaos,19,023112 2009,References,02:24:00,60,This work was supported by the National Science Foundation of China(Funds No.10702023,10832006 and 10972001),China Doctoral Science Special Foundation(Fund No.200801020).,02:24:00,61,Thanks for your interesting!,
