Observer designing for generalized synchronization of fractional order hyper-chaotic Lü system

Based on the generalized Adams-Bash-forth-Moulton predictor-corrector algorithm, dynamics of fractional order hyper-chaotic Lu system is investigated in detail. Firstly, we discussed on the range of fractional order of it to behave hyper-chaotic. Then, based on the stability theory of fractional-order system and state-observer theory, a state observer is designed to fulfill the target of tracking the states of the original chaotic fractional Lu system. Under our scheme, the response system achieved generalized linear relation synchronization with the driving system. Finally, theoretical analysis and numerical simulation are both proposed to verify the rightness of our analysis. This synchronization method can be easily extended to other chaotic systems. The classical ldquoP-Crdquo completely synchronization, the anti-synchronization, and generalized projective synchronization, can be considered as special cases of such a proposed scheme.