EEG信号数学模型与广义非线性动力学方程

Dynamic mathematic model and its solutions for epileptic EEG signal

从脑电信号与非线性动力学各种物理量之间的对应关系入手,在Van der Pol方程基础上推导了表达脑电信号的广义非线性动力学方程组系统,讨论了该系统的特性和3种求解方法,指出混沌系统内部存在吸引子突然消失(边界激变)或膨胀(内部激变)现象.

The electroencephalography （EEG） signal is assimilated with relevant physical elements in nonlinear dynamics in this paper. Then the system of general nonlinear dynamic function groups are derived from single degree Van der PoL function, which can be used to express the epileptic EEG signal. Then after discussing its properties and three kinds solutions, a concrete algorithm for calculating Lyapunov spectrum is proposed, and the internal attractor＇ s abrupt change behavior （ i. e. sudden disappearance or expansion） in the chaos system is also explained. Finally the importance and necessity of considering the proper orthogonal decomposition （POD） methods and memory characteristic is pointed out.