Dynamic Properties And Synchronization Of Fractional Nonlinear Systems

Because fractional systems have more tunable variables and more complex dynamic properties than integer-order systems,since the first chaotic Lorenz chaotic system was proposed,fractional-order chaos has been playing a role in various scientific fields.The vital role,especially in the areas of secure communications,system security,and ecological environment,have greater potential for development.In this paper,the fractional-order Arneodo chaotic system and fractional-order NBS system are selected as the research objects.The dynamic properties of the two systems are analyzed in detail,and the range of order when the two systems are in chaos is obtained through numerical calculation.The adaptive synchronization method was applied to the fractional Arneodo system.The synchronization was performed under the same order and different order.By designing a reasonable controller,the synchronization of fractional Arneodo systems with the same order and different orders are achieved.For the fractional NBS system,the adaptive synovial control synchronization method is used.Based on the adaptive control theory and the synovial control theory,a reasonable sliding mode surface and a controller are used to realize the same structure self-synchronization and fractional NBS system respectively.Different Structures Synchronization Between Order NBS System and Fractional Arneodo System.