CAJ | 학술논문

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R?ssler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。
장일개사유적정수계초혼돈계통확전위분수계형식，분석료확전적분수계계통적혼돈특성。기우분수계계통은정성이론，여추종공제사상상결합，제출일충분수계혼돈계통이구동보방법，병급출료동보공제기적해석식。이분수계R?ssler초혼돈계통여확전적분수계혼돈계통적이구동보위례，진행료수치방진，병장소제적동보응용우도상가밀해밀。이론분석여방진실험적결과표명：확전적분수계계통출현혼돈적최저계수시3.2계；응용분수계혼돈동보진행도상가밀해밀구유밀약민감，가밀후도상구유류수궤균균분포화상린상소상관성저적우량특성。
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 fractional-order system and R?ssler 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.