Fractional Order Jerk Dynamics System And Its Application In Image Encryption

In recent years, fractional calculus is used more widely. In this thesis, aiming at chaoticimage encryption application, the dynamic characteristics were carefully studied and the moreattractive results of image encryption of the fractional order Jerk system obtained.There are totally six chapters in the dissertation, and the main points for each chapter can bebriefly described as follows: Chapter1gave out the discussions about the background and thedevelopment of fractional calculus and image encryption. Based on the problems to be solved inthis study, the goals to be reached were finally put forward; In chapter2the research methods ofchaos phenomena for the Jerk dynamic system are briefly introduced. The chapter lay thefoundation for the subsequent chapters. Chapter3discussed in details the dynamics behavior ofJerk system considering the change of system parameters. It follows the pattern law of periodicmotionâ†'chaosâ†'periodic motionâ†'chaos; In chapter4time-frequency transition method isdiscussed, and fractional Jerk system is solved by using the method. We attentively discussed thedynamic behavior of fractional Jerk system with the change of system parameters. The results ofthe study show that: the change rule of dynamic behavior of the fractional Jerk system is similarto the integer-order Jerk system. However, compared with the integer Jerk system, the fractionalJerk system is obviously delayed, the chaos region is more narrow, the system is more stable. Fordifferent order values of fractional order Jerk system, domains of chaos, stability of the system isalso completely different; Chapter5mainly discusses the pseudo random of chaotic sequencesproduced by the fractional order system. The results of the study show that: the fractional ordersystem is more stable, the key space bigger, pseudo random very good, and it is very applicableto image encryption. Through histogram and correlation between adjacent pixels of encryptedimage, we found that the encrypted effect is good, and when the error of secret key is only10^-10,we can’t get the correct decrypted image; Chapter9summarizes the main results and conclusionsof the researches, and pointes out some standpoints of the thinking for the studies and makessome suggestions for future works.