A New Fractional-order Chaotic System and Its Synchronization

The chaotic behaviors in a new fractional-order system are investigated in this paper.By applying the fractional calculus theory and computer simulations, it is found that chaos does exist in the new fractional-order three-dimensional system with order less than 3.The lowest order to yield chaos in this system is 2.49.Further, based on the stability theory of the fractional-order system, projective synchronization of the new fractional-order chaotic system through designing the suitable nonlinear controller is studied.The proposed scheme is rather simple and need not compute the conditional Lyapunov exponents.Numerical results are performed to verify the effectiveness of the proposed synchronization scheme.