Anticipating synchronization of integer order and fractional order chaotic Liu systems

How to resolve the problem of long-term unpredictability for chaotic systems? Such a problem has puzzled researchers in nonlinear research fields for a long time during the last decades. Very recently, a new scheme was proposed to study the anticipating synchronization of integral order nonlinear systems for arbitrary anticipation time by H. Voss et. al. In this paper, we discussed anticipating synchronization of integer order and fractional order chaotic systems base on analyzing the error system´s stability of coupled time delayed systems. By taking the newly proposed chaotic Liu system as illustration, anticipating synchronization of coupled integer order Liu systems are discussed in detailed. Furthermore, such a new scheme was applied in the commensurate fractional-order Liu systems. We found anticipating synchronization can be achieved for arbitrary initial value and arbitrary anticipation time, since the stable region is much larger than the commensurate integer order Liu systems. Simulations experiments are proposed in the situation of integer order and fractional order coupled chaotic systems in the last section, respectively.