The synchronization method for fractional-order hyperchaotic systems

Highlights: • We propose a function cascade synchronization method for fractional-order hyperchaotic systems, which can be used to achieve the synchronization of the states of two identical fractional-order hyperchaotic systems. • The method is a more general synchronization method, which contains the complete synchronization, modified projective synchronization and anti-phase synchronization etc. • The theoretical results we obtain here may provide a possible way or some guidances to solve problems in encryption and secure communication etc. -- Abstract: In this paper, a function cascade synchronization method for fractional-order hyperchaotic systems is introduced to achieve the synchronization of two identical fractional-order hyperchaotic systems. It is shown that the method is not only theoretically rigorous, practically feasible, but also a more general one, which contains the complete synchronization, modified projective synchronization and anti-phase synchronization. In order to valid the effectiveness of the proposed method, we give two illustrative examples. Suitable controllers are designed and the function cascade synchronization for fractional-order hyperchaotic systems is achieved. Numerical simulations are performed and shown to fit with our analysis results.