一种新的分段非线性混沌映射及其性能分析

研究了logistic混沌映射的相关性质,指出当系统参数取值改变时,产生的混沌序列在相空间不具有遍历性.基于以上分析,构造了一种分段logistic混沌映射,对logistic映射和定义的分段logistic映射的分岔图和Lyapunov指数进行了研究,同时通过实验对这二种映射生成序列的随机性、相关系数、功率谱等性能进行了比较分析.在此基础上,定义了一种新的混沌系统性能评价指标——分岔迭代次数.结果表明,定义的分段logistic映射不仅具有良好的遍历性,而且对应的混沌系统相关评价指标的性能良好.关键词：混沌系统相关系数Lyapunov指数功率谱

A new piecewise nonlinear chaotic map and its performance

Properties of logistic chaotic map is studied, and it is pointed out that phase space is not ergodic when parameters of the chaotic system change. Based on these analysis, a piecewise logistic chaotic map is constructed. The bifurcation diagram and Lyapunov exponent of logistic and piecewise logistic map are studied, and the properties of randomicity, correlation coefficient and power spectrum etc. of the sequences generated by these two maps are analyzed experimentally. A new performance evaluation index for chaotic system, the bifurcation iteration time, is defined. Simulation results show that the defined piecewise logistic map is not only ergodic in phase space, and its corresponding chaotic performance evaluation indices are also better.