中文摘要：

混沌迭代序列是复杂系统动力学研究的一个分支,其序列值在不同参数条件下时会出现分叉及混沌现象.已有的方法不能同时挖掘拟合迭代序列的迭代函数的结构及其相应条件参量.文章则旨在同时挖掘出二者,主要工作包括：（1）提出了基于协同进化的异构种群挖掘模型,能融合不同种群的优势;（2）提出了新的适合挖掘迭代序列的适应度计算方式;（3）从理论上证明了多种群协同挖掘的进化难度远大于单种群进化难度,通过实验证实了在有效协同策略下,多种群进化得到的结果远优于单种群的进化结果;（4）提出3种协同进化策略,在对迭代序列的函数拟合以及参数拟合两方面,多路并行式结合策略能达到相对较优效果;（5）在合成数据和真实数据上进行了实验,证实了算法的正确性和有效性.

英文摘要：

Chaotic iterative sequence is a research direction in complex system kinetics research.The sequence may incarnate bifurcate or chaotic phenomenon under different parameter conditions.The existing methods cannot discover the iterative structure and parameters simultaneously.This study aims at mining the iterative functions and conditional parameters parallel.The main contributions include：（1） Proposes co-evolution model based on heterogeneous populations to integrate the advantages of those populations.（2） Proposes a new fitness function to mine the sequence in iterative style.（3） Theoretically proves that heterogeneous populations＇ co-evolution is more difficult than a single population＇s evolution.Experimentally proves that given effective co-evolution strategy,heterogeneous populations can obtain much better results than single population.（4） Proposes three co-evolution strategies.The cooperating strategy can archive relatively good results in terms of fitting the sequence＇s mathematic equation and the equation＇s parameters.（5） Conducts extensive experiments on both synthesized and real data to validate the correctness and efficiency of the algorithm.