Control and Synchronization of a Modified Chaotic Finance System with Integer and Non-integer Orders

In this paper, a class of modified finance chaotic systems is constructed. The stability analysis for integer and non-integer orders is investigated, and the effective chaotic range of the integer and non-integer orders is specified by the stability theory proposed by Lyapunov. In both integer and non-integer order situations, the feedback control law has the goal to asymptotically stabilize the system’s state variables to the origin, and the synchronization of the identical modified system using adaptive control is achieved with unknown constant parameters. The numerical results demonstrate that the effect of various values of the elements in the modified system with integer and non-integer orders changes the chaotic behavior to limit cycles or stable system.