复杂系统中混沌排斥子的动力学特性分析及应用研究

Analysis and Applied Study of Dynamic Characteristics of Chaotic Repeller in Complicated System

研究了由一类复杂系统排斥子所生成的时间序列的分形特征、分维值,利用相空间重构理论对排斥子所生成的混沌时序数据进行了重构· 研究了时序数据的零均值处理、傅立叶滤波对预测结果的影响,研究了预测样本值的选取对预测的相对误差、预测长度影响等相关问题· 结果表明:该模型对于这类排斥子所生成的时序数据建模和预测都具有实用性,且混沌排斥子样本数据的零均值处理对预测结果有一定的量的改变,但对排斥子样本数据进行Fourier滤波处理会降低预测的精度。

Fractal characters and fractal dimension of time series created by repeller in one complicated system were studied and the time series were reconstructed by applying theory of phase space reconstruction for chaotic times series,for purpose of modeling and prediction of time series created by chaotic repellers. The influence of zero_mean treatment, Fourier filter on prediction for time series were studied.The choice of prediction sample affects the relative error and the prediction length which were also under good concern. Result shows the modeling and prediction model provided here is practical for time series created by chaotic repellers. Zero_mean treatment has changed prediction result quantitively for chaotic repeller sample data. But using Fourier filter may decrease the prediction precision. This is theoretical and practical for study on chaotic repeller of complicated system.