基于神经网络的混沌系统状态预测

在对混沌时间序列的未来状态进行预测时,必须能够正确确定重构序列相空间时的最优时滞及最优嵌入维数,并根据序列状态的变化选定适当的模型进行预测。利用时间序列的自相关函数来确定时滞τ值,利用混沌序列嵌入维数与关联维数的关系来确定最优嵌入维数m值。在此基础上,选择神经网络模型来逼近真实系统,并采用一种新的算法来确定网络权重。最后,通过Logistic映射所产生的时间序列对所述理论进行了实证研究。

State Prediction of Chaotic System Based on ANN Model

The choice of time delay and embedding dimension is very important to the phase space reconstruction of any chaotic time series.The optimal time delay by computing autocorrelation function of time series was determined.Optimal embedding dimension was given by means of the relation between embedding dimension and correlation dimension of chaotic time series.Based on the methods above,ANN model was chosen to appoximate the given true system.At the same time,a new algorithm was applied to determine the network weights.The theory above was demonstrated through the research of time series generated by Logistic map.