Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization

In this paper, adaptive control and adaptive synchronization of an integer and fractional order new financial system with unknown constant parameters are studied. Based on Lyapunov’s stability theory, an adaptive control law is designed to asymptotically stabilize the state variables of the system to the origin in integer and fractional order cases. By the same theory, an adaptive synchronization law is designed to perform the identical synchronization of the new financial system in the cases of integer and fractional order with unknown constant parameters. Numerical simulations are carried out in order to show the efficiency of the theoretical results.