混沌多项式族的构造

Construction of chaos polynomial family

为解决Logistic混沌映射的局限性,拓宽混沌序列的生成来源,提出构造自映射混沌多项式族的解决方案。通过分析Logistic映射构造的理论基础,解析混沌多项式族构造过程,给出了构造过程的数学依据。针对控制参量系中几个典型摄动点,对所构造的混沌多项式函数族的动力学性质施行了计算机仿真研究,仿真结果表明通过引入三次自映射函数族,对自映射族进行创新构造,拓宽了混沌时间序列的来源。通过构造使Logistic映射真正形成一个函数族,这一函数族在横纵轴两个方向张开,由于函数族定义于实数空间,所以构造的函数族是(接近于)稠密的。

To resolve the limitations of the Logistic mapping and expand the generation resource of chaos seties, a solution based on the construction of chaos polynomial family function is proposed in this paper. Through expounding and analyzing the construction theory and process, the mathematic foundation of the construction is given. Computer emulation of the dynamics characteristic on several typical perturbation points in control parameter system is completed. The emulation results show that the generation resource of chaos series is expanded by the creative construction of self-mapping chaos polynomial family. By this construction, the Logistic mapping forms a true function family. This function family stretches at two directions of horizontal and vertical axis. The function family which is defined in real number space is or close to dense.