Abstract: The brain is one of nature’s most complex systems. As an important application of complex network theory in neuroscience, brain networks provide a new research direction in brain disease pathological mechanism. Synchronization has been regarded as an indicator affecting network performance, it has great impact on complex networks. In order to obtain sufficient criterion for complex synchronization of human brain network, 120 cases of alcoholism patients’brain network model are constructed using EEG kinetic equation. Then the synchronization based on Lyapunov stability theory has been certified in accordance with the constructed mode. And by making experiments on normal subjects and alcoholics, brain network synchronization status is calculated. It gives the alcohol patients and normal subjects’ synchronization status difference, which can reveal that how the alcohol abuse disorders impact on the functional structure of human brain and provide research ideas on other diseases.

Key words: synchronization, brain network, complex network, Lyapunov stability theory

摘要： 人脑是自然界最复杂的系统之一，脑网络作为复杂网络理论在神经科学中的重要应用，为脑疾病的病理机制提供了新的研究方向。同步性作为影响网络性能的指标，对于复杂网络有着重要影响。为了研究同步性在脑网络中的表现，利用EEG动力学方程对120例酗酒病人的EEG信号进行复杂网络模型构造，根据所构造的模型利用李雅普诺夫稳定性理论进行证明。并通过实验对正常人和酗酒者脑网络同步状态做出统计，给出了酗酒病人和正常人的脑网络同步差异，可以揭示酗酒疾病对于人脑在功能结构上的影响，对其他疾病提供研究思路。

关键词: 同步性, 脑网络, 复杂网络, 李雅普诺夫稳定性