基于模糊熵的组合混沌映射及其性能

Combined chaotic map based on fuzzy entropy and its performance

针对一维混沌映射混沌范围小、混沌序列不均匀、初值敏感性较差等问题,提出了一种基于模糊熵与Logistic映射的一维组合混沌映射。组合混沌映射使用模糊熵基本函数和Logistic映射作为种子映射,通过增大控制参数和取模运算得到新的混沌映射。对该映射的分岔图、Lyapunov指数、相关性、初值敏感性等性能进行仿真,结果表明,提出的混沌映射具有较大的混沌区间、较大的系统参数、近似均匀的混沌序列、较好的初值敏感性,系统动力学行为较为复杂。

For the problems of small chaotic range,uneven chaotic sequence and poor initial value sensitivity of one-dimensional chaotic map,a one-dimensional combined chaotic map based on fuzzy entropy and Logistic is proposed.The combined chaotic map uses the basic function of fuzzy entropy and the Logistic map as the seed map,and obtains a new chaotic map by increasing the control parameters and modulus operation.The simulation results of the bifurcation diagram,Lyapunov exponent,correlation and initial value sensitivity of the map show that the chaotic map proposed in this paper has large chaotic intervals,large system parameters,approximately uniform chaotic sequences,good initial value sensitivities,and complex system dynamics.