摘要
研究一类复杂变参数混沌系统时间序列的预测问题.首先构造一个变参数Logistic映射,分析变参数混沌系统的特点,指出动力学特征不断变化的这类系统不存在恒定形状的吸引子;结合Takens嵌入定理和神经网络理论,阐述神经网络方法预测具有恒定吸引子形状的混沌系统可行的原因,分析研究其用于预测变参数混沌系统的潜在问题.变参数Ikeda系统的神经网络预测试验验证了理论分析结果,试验还表明,简单增大预测训练样本数可能降低泛化预测精度,训练集的选择对这类系统的泛化预测效果影响极大,指出混沌时间序列预测实用化必须研究解决这类变参数混沌系统的预测.
Prediction of the chaotic time series generated by the complex parameter-varying systems is researched in this paper. The parameter-varying Logistic system is constructed firstly, and the properties of this kind of system are analyzed. These systems, whose parameter values change with time, do not have attractor shape invariable with time evolution because of their continually changing dynamical property. Combining the Takens＇ embedding theorem and the artificial neural networks （ANN） theory, we interprete the feasible reason that ANN method can be used to predict the chaos systems with the invariable attractor shape, and then discuss the potential problem that will be met when using ANN to predict the parameter-varying system. Experiments of forecasting the chaotic time series from parameter-varying Ikeda system using neural networks have been performed. The previous theoretical analyses are validated by the experiment results. The results also show that if only simply increasing the training data, the neural networks＇ predicting generalization ability may be reduced, the generalized predicting result on the parameter-varying system is especially seriously affected by the selected training data set. So prediction of the parameter-varying systems must be well resolved before the chaotic time series prediction can be made practical.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2008年第10期6120-6131,共12页
Acta Physica Sinica
关键词
混沌
预测
神经网络
变参数系统
chaos, prediction, artificial neural networks, parameter-varying dynamical system
