中文摘要：

人脑是极为复杂的系统,脑电（EEG）是脑内大量神经元电活动合作与竞争的综合反映,由局部和非局部频率分量构成,这些局部分量与特殊的内在神经网络状态紧密相关,在宏观上反映了脑的机能状态.脑电信号的非线性分析是近年出现的一种脑电分析方法,它反映了大脑处理信息活动的有序程度,为研究大脑高级认知活动提供了新的思路.越来越多的研究表明,传统的非线性动力学方法采用单一的参数不能充份描述脑电信号的复杂行为,多重分形用一个谱函数从不同层次描述了分形体的整体生长特征,采用多重分形方法描述系统的非线性动力学行为能够得到更多的信息.本文对不同思维模式下脑电的多重分形特性进行分析,发现EEG的奇异谱在不同的思维状态下具有差异.进一步对这种差异进行统计分析表明大脑思维的EEG多重分形特性受到人脑的思维方式的影响,EEG多重分形奇异谱强度分布反映了大脑思维模式的差异.

英文摘要：

Human brain is an extremely complicated system. Electroencephalogram （EEG） is a comprehensive reflection of the cooperation and competition of mass neuron electricity, consisted of the local and non-local frequency component. These local components, which are related with special state of the neural net, reflect the function of the brain on the macro. The nonlinearity analysis method of EEG is the are that appears recently. It reveals the degree of order to which the brain processes the information, with may provide a new way of studying the high level cognition activity of brain. More and more research indicates that traditional non-linear dynamics method using one parameter can＇t describe complicated behaviors of the EEG fully. Multifractal describes the whole growth feature of fractal with a spectrum function at many levels. Multifractal method can get more information than traditional non-linear dynamics method in describing the non-linear dynamics behavior. This paper carries on analysis of EEG in different thinking modes, All data used in this study were recorded from thirteen subjects performing baseline tasks, mental arithmetic tasks, geometric figure rotation tasks, mental letter composing tasks and counting tasks. Subjects were seated in a sound-proof, dimly-lit, room. Electrodes were placed respectively at O1, O2, P3, P4, C3, and C4, standard electrode locations in the 10- 20 system. The electrodes were connected to EEG amplifiers whose bandpass filtered the signals at 0.2-100 Hz. The EEG signals were sampled at 250 samples per second and digitized with 12 bits of accuracy. Data were recorded from each subject for duration of 10 seconds while the subject was performing a single task with his eyes open. We found many differences of singularity spectra distribution. More statistical research on such difference has proved that multifractal character of EEG is influenced by the thinking mode, and the△α. Singularity spectra distribution of EEG can reveal the thinking mode to some extent.