摘要
将一个四维的整数阶超混沌系统扩展为分数阶形式,分析了扩展的分数阶系统的混沌特性。基于分数阶系统稳定性理论,与追踪控制思想相结合,提出一种分数阶混沌系统异构同步方法,并给出了同步控制器的解析式。以分数阶Rssler超混沌系统与扩展的分数阶混沌系统的异构同步为例,进行了数值仿真,并将所提的同步应用于图像加密解密。理论分析与仿真实验的结果表明:扩展的分数阶系统出现混沌的最低阶数是3.2阶;应用分数阶混沌同步进行图像加密解密具有密钥敏感,加密后图像具有类随机均匀分布和相邻像素相关性低的优良特性。
An integral-order hyperchaotic system with four-dimension is expanded to be a fractional-order system whose chaotic behav-iors are analyzed. Based on the stability theory of fractional-order linear system and combined with the thinking of tracking control,a syn-chronization method for two fractional-order systems with different structures is proposed,and an analytic expression for synchronization controller is given. Taking the extended fractionalorder system and Rossler hyperchaotic system as example,the synchronization between them is numerical simulated. The proposed synchronization method is applied to encrypt and decrypt digital images. The theoretic analysis and simulation results show that the lowest order that extended fractional-order system appears chaos is 3. 2,and this method has many advantages for encrypting and decrypting digital images,such as sensitive secret keys,random uniform distribution of pixels and low cor-relation between adjacent pixels.
出处
《计算机技术与发展》
2015年第6期128-132,共5页
Computer Technology and Development
基金
国家自然科学基金资助项目(61262025)
云南省应用基础研究计划面上项目(2012FB118)
云南省教育科学研究基金项目(2012Y257
2013J103)
云南省软件工程重点实验室开放基金项目(2011SE09)
云南大学"中青年骨干教师培养计划"专项经费资助项目
关键词
混沌
分数阶混沌系统
混沌同步
图像加密
chaos
fractional-order chaotic system
chaotic synchronization
image encryption
