用小波熵测度Lorenz系统准周期特性

运用四阶Runge-Kutta求取了Lorenz系统的时间序列，采用小波分解与信息熵计算了时间序列的小波熵值，并用来测度系统准周期运动过程中的复杂度。计算结果表明，系统的三个运动复杂度分量均由许多大小不一、形状相似、山峰状的循环窗口组成，并且在不同的尺度上具有自相似特征，系统的小波熵序列也具有混沌性质，其运动具有准周期特性，进一步研究发现，在Lorenz系统运动的整个准周期过程中，运动复杂度的大小不同，复杂度大时，对应短准周期，复杂度小时对应于长准周期，系统的演变过程由各种不同的长准周期和短准周期交替组成。

QUASI PERIODIC PROPERTY OF LORENZ SYSTEM MEASURED BY WAVELET ENTROPY

The time series of the Lorenz chaotic sequences was calculated by fourth-order Runge-Kutta method. Then the wavelet entropy of the system was calculated by using wavelet decomposition and information entropy, which was used to measure the complexity of the system in the process of quasi-periodic motion. The results showed that for Lorenz model, its three complexities were all chaotic and composed of many cycling windows which had varied size, similar shape, peak shape. The wavelet entropy sequence of the system was also chaotic and its motion was quasi periodic. It was found that the motion complexity was different in the whole quasi periodic process of Lorenz system. When the complexity was large, it corresponded to short quasi period; when the complexity was small, it corresponded to long quasi period. The evolution process of Lorenz system was composed of different long and short quasi period.