We elaborate the concept of increasing-order synchronization and anti-synchronization of chaotic systems via an adaptive control scheme and modulation parameters. It is shown that the dynamical evolution of a third-order chaotic system can be synchronized and anti-synchronized with a fourth-order chaotic system even though their parameters are unknown. Theoretical analysis and numerical simulations are carried out to verify the results.%We elaborate the concept of increasing-order synchronization and anti-synchronization of chaotic systems via an adaptive control scheme and modulation parameters.It is shown that the dynamical evolution of a third-order chaotic system can be synchronized and anti-synchronized with a fourth-order chaotic system even though their parameters are unknown.Theoretical analysis and numerical simulations are carried out to verify the results.As the problems of synchronization and antisynchronization of chaos are interesting,nontraditional and indeed very challenging,[1] a wide variety of approaches have been proposed for chaos synchronization and anti-synchronization.[2-4] In this Letter,another type of synchronization,namely increasingorder synchronization in different chaotic systems with different orders based on parameter identification,is investigated.Such a problem exists widely in the study of cognitive processes and biological systems.[5]
展开▼
