The Research And Implementation Of Active And Passive Projective Synchronization For Chaotic Systems

Since the discovery of chaotic phenomena,its application field has been expanding continuously,and chatic synchronization is an important field of chaotic scientific research.Chaos synchronization refers to the movement trajectory of a chaotic system tend to another motion trajectory of chaotic system,and always in step.At present,chaos synchronization is widely used in physics,life science,secure communication and other desciplines.Since its great potential application in various fields,chaotic synchronization has attracted the attention of many scholars.The projective synchronization refers to a chaotic synchronization phenomenon which the chaotic synchronization is achieved between the drive system and the response system with the given scaling factor.With the uncertainty of the scaling factor,it will make the chaos system more complex.Meanwhile,it has improved the security of communication.Thus,it can be widely applied in secure communication,and other secure fields.In this paper,firstly,we proposed the active adaptive control projective synchronization scheme.Secondly,we study the passive projective synchronization scheme,and we introduce the advantages of the proposed synchronization control scheme.The main innovations of this dissertation can be summarized as follows:(1)An active adaptive projective synchronization scheme is proposed.The asymptotic stability of the error system is proved through the Lyapunov stability theorem.The active control matrix the synchronization proposed makes the adaptive active projective synchronization easy to realize.And it is easy to operate.Meanwhile,it simplifies the complicated computing process.In addition,the tenability of the proposed method is very good.We also study the scheme that can shorten the synchronization time of the error system.The proposed method can not only shorten the synchronization time,but also make the error system curve smoother.In this paper,we take Lorenz system as an example to verify the feasibility of the synchronization method through numerical simulation.(2)A passive projective synchronization is proposed.We compare the difference between the passive synchronized controlling scheme with other synchronized schemes.It has expanded the theoretical principle of the chaotic synchronized controlling theory due to the raise of passive controlling theory.The innovation points of this method are its combination of passive controlling scheme,and projective controlling scheme,which expand the application range of chaotic synchronization.Matlab simulation is adopted in this paper,and the simulation results are consistent with the theoretical derivation,which has verified the feasibility of the proposed synchronization scheme in our paper.