一个新混沌系统及错位投影同步通讯方案  

A New Chaotic System and Its Dislocated Projective Synchronization for Secure Communications

作　　者：邓玮[1] 吴艳敏[1] 方洁[1] 吴振军[1] 

机构地区：[1]郑州轻工业学院电气信息工程学院,河南郑州450002

出　　处：《数学的实践与认识》2014年第20期156-164,共9页Mathematics in Practice and Theory

基　　金：河南省2014年科技发展计划项目(142300410246);郑州轻工业学院博士基金(2013BSJJ027)

摘　　要：提出了一个新的混沌系统,该系统含有五个参数,每个状态方程均含有非线性乘积项.通过理论推导,数值仿真,Lyapunov指数、Lyapunov维数、分岔图研究其基本的动力学特性,并分析了改变参数时系统的动力学行为的变化.本文研究了该系统的错位投影同步,设计了非线性控制器,实现了两个初值不同的新系统的错位投影同步.另外,将该系统及错位投影同步方法应用到保密通信中,基于改进的混沌掩盖通讯原理,在发送端使用新系统信号对信息信号进行加密及传送,最后在同步后的接收端不失真地恢复出有用信号.数值仿真表明所设计的新的混沌系统具有复杂的动力学特性,适用于保密通讯.A new chaotic system is reported.This new system contains five system parameters and each equation contains nonlinear term.The basic properties of the new system are investigated via theoretical analysis,numerical simulation,Lyapunov exponent spectrum,bifurcation diagram,Lyapunov dimension.The different dynamic behaviors of the new system are analyzed when each system parameter is changed.This paper studies dislocated projective synchronization of the system,too.Using the Lyapunov stability theory,a nonlinear controller is presented and a kind of dislocated projective synchronization for the system is successfully completed.Then this method is applied to secure communication through improved chaotic masking.The information signal is mixed with the chaotic signal before being transmitted,and is recovered without distortion through the synchronized receiver.Simulation results show that the new system system has a complex dynamic characteristics and it is suitable for secure communications.

关 键 词：混沌 混沌同步 错位同步 保密通讯 

分 类 号：O415.5[理学—理论物理]