The Study Of Hidden Chaotic Attractors And Chaos Synchronization

The characters of hidden chaotic attractors and synchronization of real,fractional and complex chaotic systems are mainly studied in this thesis.(1)Fractional chaotic system with hidden attractors and chaos synchronizationFirstly,the LE1 system of Sprott clans is extended from integer system to fractional system and added two constant controllers,thus,the new fractional chaotic system with hidden attractors is produced.Then,based on bifurcation diagrams and phase diagrams,the characters of the proposed system are analyzed.The new system can generate one self-excited and three hidden attractors.Besides,by means of fractional finite-time stability theory,the finite-time chaos synchronization and fractional combination synchronization are accomplished.Finally,the numerical simulations illustrate the effective of proposed controllers.(2)Permanent magnet synchronous motor chaos synchronizationThe ways of PMSM finite-time chaos synchronization with completely known parameters and partly unknown parameters are illustrated in this part.Firstly,the dimensionless model of PMSM is built and analyzed.Based on Lyapunov stability theory,the chaos synchronization controller with known parameters is proposed by means of drive-response method.Then,the adaptive chaos synchronization is investigated with partly known parameter.The simulation experiments illustrate the effective and superiority of proposed controllers.(3)Secure communications based on difference function synchronization of fractional complex chaotic systemThe advantages of fractional complex chaotic system in secure communication are firstly illustrated.Based on integer difference function synchronization,the fractional difference function synchronization is presented and it is extended into complex number field.Then,by means of fractional difference function synchronization,the secure communication method of the proposed chaos synchronization are presented and four types of signal information are transmitted,such as analog signal,digital signal,voice signal and image signal.Especially,an image cryptosystem of fractional complex system is investigated.Finally,simulation experiences ensure the veracity of proposed secure communications.(4)N-system combination function projective synchronizationThe N-system combination function projective synchronization is presented.Interestingly,most of the existed synchronization types are belong to the N-system combination function projective synchronization.Finally,inspired by the real applications,time delay function projective synchronization is studied.And the general controller of time delay function projective synchronization is obtained.Numerical simulations illustrate the effectiveness of proposed controller.