基于分形自仿射特性的混沌预测方法研究

Chaotic Prediction Method Based on Self-affine of Fraction

研究了一类特殊非线性系统———混沌系统的局部预测问题。分析了分形的自仿射特性 ,将迭代函数系统(IFS)引入到混沌时间的预测中 ,从而将混沌预测问题转化为在相空间迭代寻找一个最佳的仿射算子和仿射子集 ,由此修正了最邻点的选取准则。从理论上证明了方法的可行性。结合局部超平面近似法 ,给出了迭代预测算法。数字仿真表明了该方法不仅提高了一步预测的精度 ,还具有多步较好的预测能力。

Local forecast of a special non-linear system chaotic system is studied in this paper. After the analysis of self affinity of fraction, the prediction of the chaotic series is converted to finding a best self affine operator and subset based on applying the IFS, thus the rule of neighbor points is modified. Basing on the hyper plane method, the iterated prediction algorithm is deduced. The feasibility is proved theoretically. Simulation shows the method not only improves the precision of one step prediction, also possesses good multi step ability of prediction.