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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.
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Keywords:
- neural mass model /
- synaptic plasticity /
- bifurcation analysis /
- dynamics
[1] Hashemi M, Valizadeh A, Azizi Y 2012 Phys. Rev. E 85 021917
[2] Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 物理学报 61 020503]
[3] Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 物理学报 59 5319]
[4] Gu H G, Hui L, 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 H 1974 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 62 020202]
[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 2011 Neural Comput. 23 3232
[22] Spiegler A, Kiebel S J, Atay F M, Knösche T R 2010 NeuroImage 52 1041
[23] Goodfellow M, Schindler K, Baier G 2011 NeuroImage 55 920
[24] Goodfellow M, Schindler K, Baier G 2012 NeuroImage 59 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 Neuropsychopharmacology 33 18
[28] Žiburkus 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
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[1] Hashemi M, Valizadeh A, Azizi Y 2012 Phys. Rev. E 85 021917
[2] Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 物理学报 61 020503]
[3] Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 物理学报 59 5319]
[4] Gu H G, Hui L, 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 H 1974 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 62 020202]
[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 2011 Neural Comput. 23 3232
[22] Spiegler A, Kiebel S J, Atay F M, Knösche T R 2010 NeuroImage 52 1041
[23] Goodfellow M, Schindler K, Baier G 2011 NeuroImage 55 920
[24] Goodfellow M, Schindler K, Baier G 2012 NeuroImage 59 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 Neuropsychopharmacology 33 18
[28] Žiburkus 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
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