CAJ | 학술논문

对一个同量分数阶超混沌 Qi 系统进行仿真分析，绘制了该分数阶系统的相轨迹图、Poincaré截面映射图、Lyapunov 指数谱图和分岔图，仿真结果验证了该分数阶系统的混沌特性。在此基础上，将该分数阶超混沌 Qi 系统应用于数字图像加密，并对密文的直方图、相邻像素相关性、密钥敏感性等进行分析。结果表明：基于分数阶超混沌Qi系统的图像加密算法具有密钥空间大、安全性高等特点。
대일개동량분수계초혼돈 Qi 계통진행방진분석，회제료해분수계계통적상궤적도、Poincaré절면영사도、Lyapunov 지수보도화분차도，방진결과험증료해분수계계통적혼돈특성。재차기출상，장해분수계초혼돈 Qi 계통응용우수자도상가밀，병대밀문적직방도、상린상소상관성、밀약민감성등진행분석。결과표명：기우분수계초혼돈Qi계통적도상가밀산법구유밀약공간대、안전성고등특점。
A commensurate fractional-order hyper-chaotic Qi system was analyzed by means of numerical simulation in-cluding drawing its phase portraits,Poincaré maps,Lyapunov exponent spectra and bifurcation diagrams. Simulation results verified the chaotic characteristics of the fractional order system. After that the application of the fractional-order hyper-chaotic Qi system to image encryption was investigated,and the histogram,adjacent pixels correlation,key sensitivity of the ciphertext were analyzed. Results show that the algorithm of image encryption based on fractional hyper-chaotic Qi system has a large key space and high security.