The Time Series Of The Sand Pile Model And The Critical State In The Brain's Cognitive Activities

The self-organized critical phenomenon exists widely in a variety of practical complex system,ranging from physics,biology,economy,to social science and ecology,and also plays an important role in the brain cognitive activities.During the past decades,there has been a surge of interest in the study of self-organized criticality.In order to understand the self-organized critical phenomenon better,we study the time series of the sandpile model and the self-organized critical state of the EEG signal of the brain cognitive activities by both numerical simulations and experimental data analysis.The main contents are summarized as following:1.We study the power-law property of the time series in sandpile model.The power-law distribution is a basic characteristic in a system having self-organized criticality,and it has been widely used to reveal the existence of self-organized criticality in systems.However,in some natural phenomena,such as solar flares,the spatial data is difficult to collect,and we can only get the time information of the observed system.However,the collected data cannot directly be used to compare the data with the model.Therefore,the key to our work is how to obtain the statistical characteristics of real systems from the finite time information.In sandpile model,the spatio-temporal behavior of avalanche is transformed into the signal of time-resolved series,and the mechanism of the power law behavior is studied.Based upon the sandpile model under unified time scale,the temporal sequences of the critical unstable node number are produced,and the corresponding energy distributions are calculated.The result shows that the power law behavior of the energy distribution can be obviously determined at some proper size of the time window and large energy division.The power law characteristic of the calculated energy distribution can be clearly shown when the drive size is small or the system size is large.The above results may provide a theoretical basis or useful method to reveal the power-law characteristic hidden in time sequences in the nature.2.We study the self-organized criticality in the cerebral cortex EEG signals of the brain cognitive activities.The organizing principle and activity rhythm of cognitive activities of the neurons signal is closely related to the working mechanism in the brain.The criticality of the EEG signals in cerebral cortex is meaningful to understand the brain cognitive activities.Therefore,in the second half of the work,the criticality in the process of brain cognitive activities is studied.We analyse the energy distribution of the EEG signal in electrode,and statistics the number of the subjects showing power-law behavior in different brain regions and electrodes.The results show that the most of the subjects show better power-laws behavior in the front and central brain,but there are a few subjects in the parietal and posterior brain.In order to understand this phenomenon,we further study the Event-related potential(ERP).The result shows that the sites exhibiting better power-law have small P3 wave,that is,these sites are weakly involved in the process of cognition.These results provide new evidences that the rest states of brain exhibit critical behavior.