Complex dynamical behavior and modified projective synchronization in fractional-order hyper-chaotic complex Lü system

• The fractional-order hyper-chaotic complex Lu¨ system is proposed for the first time.
• The variation of both the system parameters and the fractional order can induce bifurcations.
• The modified projective synchronization of fractional-order hyper-chaotic complex Lu¨ system is achieved.

In this paper, a dynamic system, the fractional-order hyper-chaotic complex Lü system is proposed for the first time and its rich dynamics are investigated through numerical simulations. It is found that the variation of both the system parameters and the fractional order can induce bifurcations, and the parameter ranges of chaos are different. Furthermore, based on the Open-Plus-Closed-Loop (OPCL) technique and the stability theory of fractional-order dynamical system, a scheme of modified projective synchronization (MPS) for the fractional-order hyper-chaotic complex Lü system is presented, which can effectively achieve modified projective synchronization in a class of high dimensional fractional-order systems. Examples of numerical simulations are presented to show the validity of the proposed control strategy.