基于分岔理论的突触可塑性对神经群动力学特性调控规律研究
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摘要
神经群模型是典型的非线性系统,具有丰富而复杂的动力学行为模式.神经群兴奋性和抑制性突触具有可塑性,并对神经群动力学特性具有重要调控作用,研究突触可塑性对神经群动力学特性的调控规律具有重要意义.本文基于分岔理论,通过神经群模型兴奋性和抑制性突触增益的余维一分岔分析,分别给出了神经群运行于单稳、双稳、正常和异常极限环振荡状态的兴奋性和抑制性突触增益的单参数区间;进而通过兴奋性和抑制性突触增益的余维二分岔分析给出了神经群运行于上述多种状态的双参数区域.上述结果定量剖析了兴奋性与抑制性突触可塑性及二者的相互作用对神经群动力学特性的调控规律,揭示了兴奋性与抑制性的动态平衡在神经电活动调控中所扮演的关键角色,仿真结果验证了分岔分析的正确性.本文的研究对理解突触可塑性在脑功能的维持及各种神经疾病的诱发机制中所扮演的角色具有重要参考价值.
Neural mass model is a typical nonlinear system with rich and complex dynamics. Up to now, most bifurcation researches of neural mass model(NMM) have focused on the influence of input or connection parameters between subpopulations on the dynamics of NMM. Actually, the synaptic strength is varied temporally, owing to synaptic plasticity,and plays a crucial role in regulating the dynamics of NMM. However, there are no researches on synaptic strength bifurcation analysis of NMM, and how excitatory and inhibitory synaptic plasticity exerts an influence on the dynamics of NMM is still little known. Motivated by this idea, the bifurcation analysis of excitatory and inhibitory synaptic strength of NMM is conducted in this study. Firstly, codimension-one bifurcation analyses of excitatory and inhibitory synaptic strengths are performed, respectively, through which the parameters regions of stability, bistablility, normal and abnormal oscillation are determined. Secondly, codimension-two bifurcation analysis is conducted, through which we can further gain an insight into the influence of the interaction between excitatory and inhibitory synaptic strengths on the dynamics of NMM. Finally, the bifurcation analysis results is verified by the simulation results. This study of bifurcation reveals two kinds of oscillation mechanisms: limit cycle oscillation mechanism and input-induced transition between two states of the bistability.
Neural mass model is a typical nonlinear system with rich and complex dynamics. Up to now, most bifurcation researches of neural mass model(NMM) have focused on the influence of input or connection parameters between subpopulations on the dynamics of NMM. Actually, the synaptic strength is varied temporally, owing to synaptic plasticity,and plays a crucial role in regulating the dynamics of NMM. However, there are no researches on synaptic strength bifurcation analysis of NMM, and how excitatory and inhibitory synaptic plasticity exerts an influence on the dynamics of NMM is still little known. Motivated by this idea, the bifurcation analysis of excitatory and inhibitory synaptic strength of NMM is conducted in this study. Firstly, codimension-one bifurcation analyses of excitatory and inhibitory synaptic strengths are performed, respectively, through which the parameters regions of stability, bistablility, normal and abnormal oscillation are determined. Secondly, codimension-two bifurcation analysis is conducted, through which we can further gain an insight into the influence of the interaction between excitatory and inhibitory synaptic strengths on the dynamics of NMM. Finally, the bifurcation analysis results is verified by the simulation results. This study of bifurcation reveals two kinds of oscillation mechanisms: limit cycle oscillation mechanism and input-induced transition between two states of the bistability.
引文
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[3]Yang Z Q 2010 Acta Phys.Sin.59 5319(in Chinese)[杨卓琴2010物理学报59 5319]
[4]GuH G,HuiL,Jia B 2012 Acta Phys.Sin.61 080504(in Chinese)[古华光,惠磊,贾冰2012物理学报61 080504]
[5]Lopes da Silva F H,Hoeks A,Smits H,Zetterberg L H1974 Kybernetik 15 27
[6]Jansen B H,Rit V G 1995 Biol.Cybern.73 357
[7]Liu X,Ma B W,Liu H J 2013 Acta Phys.Sin.62 020202(in Chinese)[刘仙,马百旺,刘会军2013物理学报62020202]
[8]Zheng Y,Luo J J,Harris S,Kennerley A,Berwick J,Billings S A,Mayhew J 2012 NeuroImage 63 81
[9]Wang J S,Xu Y 2014 Acta Phys.Sin.63 068701(in Chinese)[王俊松,徐瑶2014物理学报63 068701]
[10]Stephan K E,Kasper L,Harrison L M,Daunizeau J,den Ouden H E,Breakspear M,Friston K J 2008 NeuroImage 42 649
[11]David O,Friston K J 2003 NeuroImage 20 1743
[12]Deco G,Jirsa V K,Robinson P A,Breakspear M,Friston K 2008 PLoS.Comput.Biol.4 e1000092
[13]Destexhe A,Sejnowski T J 2009 Biol.Cybern.101 1
[14]Cui D,Li X L,Ji X Q,Liu L X 2011 Sci.China:Infom.Sci.54 1283(in Chinese)[崔冬,李小俚,吉学青,刘兰祥2011中国科学:信息科学54 1283]
[15]Uhlhaas P J,Singer W 2010 Nat.Rev.Neurosci.11 100
[16]Schnitzler A,Gross J 2005 Nat.Rev.Neurosci.6 285
[17]Paulo C,Rech 2012 Chin.Phys.Lett.29 060506
[18]Liu X,Gao Q,Li X L 2014 Chin.Phys.B 23 010202
[19]Wang H X,He C 2003 Chin.Phys.B 12 259
[20]Grimbert F,Faugeras O 2006 Neural Comput.18 3052
[21]Touboul J,Wendling F,Chauvel P,Faugeras O 2011Neural Comput.23 3232
[22]Spiegler A,Kiebel S J,Atay F M,Knsche T R 2010NeuroImage 52 1041
[23]Goodfellow M,Schindler K,Baier G 2011 NeuroImage55 920
[24]Goodfellow M,Schindler K,Baier G 2012 NeuroImage59 2644
[25]Coombes S 2010 NeuroImage 52 731
[26]Abbott L F,Nelson S B 2000 Nat.Neurosci.3 1178
[27]Citri A,Malenka R C 2007 Neuropsychopharmacology33 18
[28]Ziburkus J,Cressman J R,Schiff S J 2013 J.Neurophysiol.109 1296
[29]Dhooge A,Govaerts W,Kuznetsov Y A 2003 ACM Trans.Math.Softw.29 141