一类三次多项式混沌映射的判定及性能分析

Determination and Properties Analysis of a Cubic Polynomial Chaotic Map

该文给出了一般3次多项式映射与分段线性混沌映射拓扑共轭的充分条件,从而间接地给出了一般3次多项式成为混沌系统的充分条件。进一步对拓扑共轭的分段线性映射和多项式映射的均匀性、结构复杂性和随机性进行了分析,结果显示分段线性映射的均匀性优于多项式映射,多项式映射的随机性优于分段线性映射,在结构复杂性方面,二者没有显著差异,但量化方法对二者的结构复杂性影响显著。

This paper provides the sufficient conditions for topological conjugation between the general cubic polynomial maps and a piecewise linear chaotic map,then provides indirectly the sufficient conditions that make the cubic polynomial maps be chaotic.This paper analyzes further the uniformity,structural complexity and randomness of the piecewise linear map and cubic polynomial maps of topological conjugation.The results show that the uniformity of the piecewise linear map is better than the polynomial maps while the randomness of the polynomial maps is superior to the piecewise linear map.As for the structural complexity,there is no significant difference between the two kinds of systems,but it should be noted that the quantitative method makes a significant impact on the structure complexity of the systems.