Hopf Bifurcation And Generalized Synchronization Of The Delayed Coupled Lorenz-rossler Systems

Coupled dynamics of the classical Lorenz system and Rossler system plays the ba-sic role of the studying of the synchronization of the coupling chaotic system. Under the support of the National Natural Science Foundation of China (Grant No:10702065), the dynamics of the coupled Lorenz-Rossler systems with coupling delay is considered em-ploying the analysis software of the delayed dynamical systems-DDE-BIFTOOL in this dissertation, it reveals the effects of the coupling and delay on the dynamics of the coupled systems. For the unidirectionally delayed coupled systems, only the coupling has effect on the equilibria and their stability, but delay can't effect their local dynamics. But for the bidirectionally delayed coupled systems, not only the coupling but also delay can effect their local dynamics, the stable Hopf bifurcation occurs due to them and thus the gen-eralized synchronization of them is obatined, it implies that the delay can restrain their chaotic behavior.