Logistic混沌系统的熵特性研究  

Research on the entropy of logistic chaos

作　　者：潘欣裕[1,2] 赵鹤鸣[2] 

机构地区：[1]苏州科技学院电子与信息工程学院,苏州215011 [2]苏州大学电子信息学院,苏州215021

出　　处：《物理学报》2012年第20期105-111,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61071215);江苏省研究生科研创新计划(批准号:CXZZ12_0815);苏州市应用基础研究项目(批准号:SYG201033)资助的课题~~

摘　　要：作为形式上相对较为简单的一维混沌函数,Logistic系统在很多领域有着重要的应用.本文主要分析了Logistic系统的熵稳定特性,对不同参数μ和系统初值形成的Logistic序列,进行了统计分类,得到了一系列的熵值,并详细分析了熵的分布情况.数值仿真结果表明,Logistic系统的熵由参数μ决定,而与系统初值基本无关,且当参数μ取值接近上界(μ=4)时,序列分布越趋于均匀,熵也接近理论极限值.As a simple one-dimensional chaotic system, logistic map has some important applications in many fields. The stable entropy characteristic of logistic function is proposed in this paper. A series of logistic sequence entropy, calculated under different initial values and values of parameter μ, is found to have some special distributions. A great number of numerical simulations prove that the entropy is determined by parameter μ, and it is irrelevant with initial value. The logistic sequence becomes a uniform distribution, and its entropy is close to a maximum, when μ is increased to 4. Thereby the stationary quality of logistic chas can be speculated to some extent.

关 键 词：Logistic系统 混沌 熵 

分 类 号：O415.5[理学—理论物理]