Triangular Synchronization And Generalized Synchronization Of Chaotic Systems

Recently, with the fast development of chaos theory in nonlinear science and the great application value of chaos synchronization in secure communication, chaos synchronization has become a hotspot of scholars' study.Combining the methods of theoretical deduction and numerical simulation, this paper studies triangular chaos synchronization and the generalized synchronization of hyperchaotic systems. The author has the following work:The triangular form of chaotic system and the synchronization method of chaotic system in this form are studied. A class of Sprott circuit systems which are typical triangular chaotic systems are introduced; after obtaining the triangular forms of Lüand Sprott-B systems via Lie derivative, the nonlinear controllers of the responser in synchronization systems are designed, therefore both the synchronization of Genesio-Tesi and Coullet systems and the generalized synchronization of Lüand Sprott-B systems are realized in two feedback ways. Results of numerical simulations validate the effectiveness of the given synchronization methods. The two schemes have better generality and the driver and responser can exchange positions, so they have some application prospects.Based on feedback method and pole placement technology in control theory, the generalized synchronization of hyperchaotic system and its application in secure communication are studied theoretically. Taking hyperchaotic Chen system as an example, generalized synchronization of hyperchaotic system is realized successfully; the synchronous speed between driver and responser can be improved via placing the pole of error system; numerical simulations validate the correctness of the proposed synchronization method. Taking the chaotic masking as an example, the secure communication of generalized synchronization for hyperchaotic Chen system is simulated, which confirms the validity of the secure communication scheme. For the use of pole placement technology in the generalized synchronization, the secure communication scheme proposed in the paper has huge flexibility.