一个二次多项式混沌系统的均匀化及其熵分析

利用已有理论给出了一个二次多项式混沌系统,证明了该系统与Tent映射拓扑共轭,给出了该混沌系统的概率密度函数;并根据此概率密度函数,得到了轨道均匀分布的反三角函数映射;对均匀化前后的混沌系统在不同参数下产生序列的信息熵、Kolmogorov熵、离散熵的特性进行了分析,结果显示均匀化后产生的混沌序列混沌程度不改变且具有更好的均匀性.

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In this paper, firstly we construct a quadratic chaotic system and prove that it is a topological conjugate system of Tent map. Secondly, having analyzed the probability density function of the system, we propose an anti-trigonometric function map. Additionally, the performances of the quadratic chaotic system such as information entropy, Kolmogorov entropy and discrete entropy are tested for both the original systems and the homogenized systems with different parameters. Numerical simulations show that the information entropy of the uniformly distributed sequence is close to the theoretical limit and the discrete entropy remains unchanged. This result shows that the homogenization method is effective. In conclusion, the chaotic sequence after homogenization not only inherits the diverse properties of the original sequence, but also exhibits better uniformity.