Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters

In this paper, an adaptive control scheme is developed to study the add order synchronization and the add order anti-synchronization behavior between two different dimensional fractional order chaotic systems with fully uncertain parameters. This design of adaptive controller is based on the Lyapunov stability theory. Analytic expression for the controller with its adaptive laws of parameters is shown. The adaptive add order synchronization and add order antisynchronization between two fractional order chaotic systems are used to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are used to verify the results.