简单层次网络上的自组织临界行为
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摘要
采用改进的二维格子地震(OFC)模型研究了简单两层网络上的雪崩行为.考虑到层间的性质或功能有差异,在OFC模型中引进层内控制参量α和层间控制参量β,得到其雪崩大小在一定范围内满足幂律分布,超出一定的值,系统便不再处于自组织临界态,而处于超临界态.另外,膜电位平均值的时间序列的功率谱也近似满足1/5幂律行为.
The avalanche behavior of simple two-level network is studied by using the improved OFC model in this paper.Considering the different nature or function between levels,two different control parameters,and are introduced to express control parameters of level internal and levels respectively.The conclusion is reached that the avalanche distribution obeys the power-law distribution within a certain range.The system will not be in the self-organized critical state,but in the supercritical state when the parameters exceed the certain value.Otherwise,the power spectrum of time series of the average membrane potential approximately obeys the power-law behavior.
The avalanche behavior of simple two-level network is studied by using the improved OFC model in this paper.Considering the different nature or function between levels,two different control parameters,and are introduced to express control parameters of level internal and levels respectively.The conclusion is reached that the avalanche distribution obeys the power-law distribution within a certain range.The system will not be in the self-organized critical state,but in the supercritical state when the parameters exceed the certain value.Otherwise,the power spectrum of time series of the average membrane potential approximately obeys the power-law behavior.
引文
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[13]Li Wenyuan,Lin Yongjing,Liu Ying.The structure of weighted small-world networks[J].Physica A:Statistical Mechanics and its Applications,2007,376:708-718.
[14]Lu Xin Biao,Wang Xiao Fan,Li Xiang,et al.Synchronization in weighted complex networks:Heterogeneity and synchronizability[J].Physica A:Statistical Mechanics and its Applications,2006,370(2):381-389.
[15]Zhang G Q,Tirnakli U,Wang L,et al.Self organized criticality in a modified Olami-Feder-Christensen model[J].Eur Phys J B,2011,82(1):83-89.
[16]Yamamoto T,Yoshino H,Kawamura H.Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes[J].Eur Phy J B,2010,77:559-564.
[17]Christensen K,Moloney N R.Complexity and Criticality[M].England,London:Imperial college press,2005.
[2]Gutenberg B,Richter C F.Magnitude and energy of earthquakes[J].Ann Geofis,1956,9:1-15.
[3]Raup M D.The nemesis affair:a story of the death of dinosaurs and the ways of science[J].Science,1986,251:1530.
[4]伯努瓦.B.曼得布罗特.大自然的分形几何[M].陈守吉,凌复华,译.上海:上海远东出版社,1998.
[5]Tang C,Bak P.Critical exponents and scaling relations for self-organized critical phenomena[J].Phys Rev Lett,1988,60(23):2347-2350.
[6]Burridge R,Knopoff L.Model and theoretical seismicity[J].Bull Seismol Soc Am,1967,57:341-371.
[7]Olami Z,Feder S,Christensen K.Self-organized criticality in a continuous,nonconservative cellular automaton modeling earth-quakes[J].Phys Rev Lett,1992,68(8):1244-1247.
[8]Christense K,Olami Z.Scaling,phasetransitions and nonuniversality in a self-organized critical cellular-automaton model[J].Phys Rev A,1992,46(4):1829-1838.
[9]Bak P,Sneppen K.Punctuated equilibrium and criticality in a simple model of evolution[J].Phys Rev Lett,1993,71:4083-4086.
[10]Hopfield John J.Neurons,dynamics and computation[J].Physics Today,1994,47(2):40.
[11]Stephan K E,Kamper L,Bozkurt A,et al.Advanced database methology for the collation of connectivity data on the macaque brain(CoCoMac)[J].Phil Trans R Soc Lond B Biol Sci,2001,356:1159-1186.
[12]Scannell J W,Blackmore C,Young M P.Analysis of connectivity in the cat cerebral cortex[J].J Neurosci,1995,15:1463-1483.
[13]Li Wenyuan,Lin Yongjing,Liu Ying.The structure of weighted small-world networks[J].Physica A:Statistical Mechanics and its Applications,2007,376:708-718.
[14]Lu Xin Biao,Wang Xiao Fan,Li Xiang,et al.Synchronization in weighted complex networks:Heterogeneity and synchronizability[J].Physica A:Statistical Mechanics and its Applications,2006,370(2):381-389.
[15]Zhang G Q,Tirnakli U,Wang L,et al.Self organized criticality in a modified Olami-Feder-Christensen model[J].Eur Phys J B,2011,82(1):83-89.
[16]Yamamoto T,Yoshino H,Kawamura H.Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes[J].Eur Phy J B,2010,77:559-564.
[17]Christensen K,Moloney N R.Complexity and Criticality[M].England,London:Imperial college press,2005.
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