一种高复杂性的混沌序列

摘要

针对传统混沌映射初值迭代简单、满映射的参数区间窄、复杂性不高,提出了一种高复杂性的新型混沌序列.将改进型Logistic和Chebyshev一维混沌映射进行错位相乘,混沌映射由普通的二阶或者余弦映射关系变为二阶与余弦乘积关系,且混沌映射表达式由原来的一阶差分扩展为二阶差分,从而提高了混沌系统的复杂性.对该序列的非线性动力学特性以及混沌特性进行仿真,仿真结果表明,新混沌序列具有更加复杂的混沌吸引子、更强的初始值敏感性和随机性、近似熵值更高、复杂性更高,可应用在混沌保密通信和对信息安全要求高的领域.%The sequence generated by the traditional single chaotic map has the problem of simple initial iteration,the param-eter interval is narrow and low complexity,a new chaotic sequence with high complexity is proposed.The improved one-di-mensional chaotic Logistic and Chebyshev mapping is multiplied,chaotic mapped by ordinary second-order or cosine map-ping relationship is transformed into the relationship between the product of second-order with cosine,chaotic mapping ex-pression by the original first order difference becomes second order difference,thus increases the complexity of chaotic sys-tem.The nonlinear dynamics characteristics and chaotic sequence are simulated by computer.The results show that the new chaotic sequence has more complex chaotic attractors.It has stronger initial value sensitivity and randomness,and it also has higher approximate entropy value and chaotic sequence complexity.This new sequence can be widely applied in chaotic se-cure communications and other high requirements for information security fields.