改进的Logistic映射及其动力学特性  

Modified Logistic Map and Its Dynamic Performances

作　　者：韩春艳[1,2] 禹思敏[1] 

机构地区：[1]广东工业大学自动化学院,广东广州510006 [2]滨州学院物理与电子科学系,山东滨州256603

出　　处：《中国海洋大学学报（自然科学版）》2015年第5期120-125,共6页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(61172023;61271064);浙江省自然科学重点基金项目(LZ12F01001);滨州学院科研基金项目(BZXYG1205)资助

摘　　要：为了获得性能良好的混沌伪随机序列,分别采用尺度变换、构建鲁棒性系统和复合映射的方法对Logistic映射进行改进。Logistic映射的尺度变换可任意扩展满映射区间和混沌区间,能够改善序列的随机特性,增大密钥空间;构建鲁棒性系统可使其在一定条件下呈现具有恒定Lyapunov指数的恒定混沌状态,形成鲁棒混沌映射;复合映射能够成倍提高Lyapunov指数,可改善映射的初值敏感性和随机性。因此,改进的Logistic映射可作为伪随机序列发生器的随机信号源,在保密通信、密码系统和计算机等领域将有良好的应用潜力。In order to generate good chaotic pseudo-random sequences, we modified the Logistic map u- sing scale transformation, constructing robust system and complex mapping respectively. Scale transfor- mation for the Logistic map can arbitrarily expand its mapping region and chaotic range, improve sto- chastic characteristics and increase key space for its sequences. Constructing robust system will enable it to present constant chaos state with constant Lyapunov exponent, thereby forming a robust chaotic map. While complex map can increase its Lyapunov exponent by times and can improve its initial value sensitivity and randomness. Therefore, the modified Logistic map can be used as random sequence signal sources, which has application notential for secret communications, cryptosystems and computers.

关 键 词：混沌 LOGISTIC映射 鲁棒混沌映射 复合映射 

分 类 号：O415.5[理学—理论物理]