Study On Synchronization Model Of Chaotic And Hyperchaotic Systems

As a special nonlinear phenomenon,chaos has attracted wide attention since its discovery.Compared with chaotic systems,hyperchaotic systems have higher dimensional chaotic attractors,which contain more complex dynamic behavior.In addition,chaotic systems are extremely sensitive to initial values,and their trajectories are unpredictable.Chaos synchronization can keep the motion trajectories of two or more(hyper)chaotic systems consistent.At present,this phenomenon has been applied in many fields,such as secure communication and chaotic radar.Therefore,the study on the new synchronization method has not only theoretical value,but also practical significance.This paper proposes three new types of chaos synchronization: dual generalized synchronization,modulus synchronization,and synchronization of n cascade-coupled chaotic systems.Aiming at different synchronization methods,typical chaotic systems and newly designed hyperchaotic systems are used to verify the validity of the theory.Among them,a hyperchaotic real number system is constructed for modulus synchronization experiments,and the corresponding complex system are obtained by complexing the system.The analysis of their dynamic characteristics showed that both systems met the hyperchaotic state.The specific work is as follows:(1)At present,chaos synchronization models are mainly single-drive and single-response models.This paper proposes dual generalized synchronization,that is,dual-drive and dual-response synchronization models.A high-order system is obtained by linearly coupling two different chaotic systems and applying the principle of diagonalization of matrices to "upgrade".It is then applied to traditional generalized synchronization.The advantage is that the signals received by the response system contain the signals of the two drive systems at the same time,so the synchronization process becomes more complicated and difficult.Dual generalized synchronization has certain significance in designing secure communication schemes.(2)The synchronization of real-drive and real-response systems,the synchronization of complex-drive and complex-response systems,and the synchronization of real-drive and complex-response systems have all been achieved.And researching the synchronization of complex-driven and real-response systems is an interesting and meaningful issue.The modulus of a complex system variable is one of its important parameters and has been applied in the fields of secure communication.Therefore,it is necessary to further study the modulus synchronization.This paper proposes a new chaotic synchronization method—modulus synchronization.Using Lyapunov stability theory,an adaptive controller is designed to achieve synchronization between the complex drive system and the real response system.A hyperchaotic real system and its corresponding complex system are constructed and applied to modulus synchronization.Matlab simulation verifies the effectiveness of the algorithm..When compared with the existing works,it is significant for forming a close relationship between complex chaos and real chaos.The proposed modulus synchronization between the hyperchaotic complex systems and the hyperchaotic real systems can provide a new choice for secure communication and engineering science.(3)The existing synchronization has been acquired for 2 chaotic systems,and the synchronization problems of n chaotic systems are yet to be investigated.In this paper,we investigate a novel synchronization method,which consists of n(n?2)cascade-coupled chaotic systems.Furthermore,as the number of chaotic systems decreases from n to 2,the proposed synchronization will transform into bi-directional coupling synchronization.Based on Lyapunov stability theory,a general criterion is proposed for choosing the appropriate coupling parameters to ensure cascading synchronization.Compared with dual generalized synchronization and modulus synchronization,the synchronization model is easier to verify in software and the hardware implementation is less difficult after the effective interval of the coupling parameters is determined.