document: Modification for synchronization of Rossler and Chen chaotic systems Active control is an effective method for making two identical Rossler and Chen systems be synchronized . However , this method works only for a certain class of chaotic systems with known parameters both in drive systems and response systems . Modification based on Lyapunov stability theory is proposed in order to overcome this limitation . An adaptive synchronization controller , which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized in the presence of system 's unknown constant parameters , is derived . Especially , when some unknown parameters are positive , we can make the controller more simple , besides , the controller is independent of those positive uncertain parameters . At last , when the condition that arbitrary unknown parameters in two systems are identical constants is cancelled , we demonstrate that it is possible to synchronize two chaotic systems . All results are proved using a well-known Lyapunov stability theorem . Numerical simulations are given to validate the proposed synchronization approach
doc_bio_tags: O O B O O O B I I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O
extractive_keyphrases: synchronization chen chaotic systems active control response systems lyapunov stability theory
abstractive_keyphrases: rossler chaotic systems adaptive synchronization controller global asymptotic synchronization