A new fractional-order hyperchaotic system and its modified projective synchronization

A new four-dimensional (4D) autonomous hyperchaotic system is investigated at first. It is found that the fractional-order version of the system goes through periodical status to chaos and hyperchaos while the order number q is increased. We verify the realizability of the new fractional-order hyperchaotic system via a practical electronic circuit. Furthermore, an active integral sliding mode control (ISMC) scheme is proposed to achieve the modified projective synchronization (MPS) of two different fractional-order hyperchaotic systems. The sliding mode controller of MPS is derived based on the stability theory of the fractional-order system and Lyapunov stability theorem. The presented method can guarantee the synchronization error asymptotically stable and enhance the robustness of MPS. Finally, the MPS between the fractional-order Chen hyperchaotic system and the new fractional-order hyperchaotic system is considered as an example, our simulation results demonstrate the effectiveness and robustness of the proposed method.