相空间导数重构法的探讨

Study on the Derivative Reconstruction Method

探讨了导数重构法在实际应用中存在的问题 :重构相空间的坐标间尺度差异太大及由时间序列求导时产生的计算误差太强。这两个问题重构相空间受到强烈的噪声干扰 ,而无法用来表征系统的混沌特征。提出针对性的改进措施 :一是采取坐标归一化措施 ,二是采用曲线拟合对时间序列求导。实际的重构证明 ,改进导数重构法有效地克服了导数重构法的实际应用困难 。

The paper discussed the two problems existing in application of derivative reconstruction method:one is the big difference presented among the coordinate scales of reconstruction phase space,and the other is the significant calculation errors resulted in derivation of the time series. These two problems make the phase space reconstructed suffer a heavy noise disturbance so that it can not be applied to characterize the chaotic system. To solve the above problems,two measures were taken,i.e.,regularization of the coordinates and curve fitting derivation from the time series. The practice of reconstruction shows that the improved method effectively overcomes the shortcomings of derivative reconstruction method and can be efficiently used to reveal the chaotic characteristics of systems.