多变量时间序列复杂系统的相空间重构

根据单变量时间序列相空间重构思想 ,提出了多变量时间序列描述的复杂系统的相空间延迟重构方法 .对每一分量的时间序列 ,分别利用互信息最小法确定最佳延迟时间间隔 ,最小嵌入维数的选取方法是单变量时间序列情况下虚假邻点法的推广 .给出了q阶广义关联积分和q阶广义关联维数的计算公式 ,并证明了广义关联维数与所用范数无关 .计算了Lorenz系统按前 2个变量进行重构时的最佳延迟时间间隔和最小嵌入维数 .计算结果表明 ,用多变量时间序列重构比用单变量时间序列重构所需的数据长度要短得多且在方法上更有效

Phase space reconstruction of complex systems based on multivariate time series

According to the phase space reconstruction of a single variate time series, a new phase space delay reconstruction method based on multivariate time series of complex systems is proposed. The good time delay is chosen for each scalar time series by mutual information. The method to get the minimum embedding dimension by the false neighbor in single variate case is popularized to multivariate case. The formulation of generalized correlation integration and generalized correlation dimension of order q are proposed, which are not influenced by norm. Simulated by the Lorenz system with the first two variates, the good time delay, the minimum embedding dimension and the generalized correlation dimensions of order 1,2,3 are calculated. The results confirm that the length of the time series is shorter and the method is more efficient in reconstruction based on multivariate time series than single variate time series.