International Journal of Sciences: Basic and Applied Research (IJSBAR) ISSN 2307-4531 (Print & Online) http://gssrr.org/index.php?journal=JournalOfBasicAndApplied ------------------------------------------------------------------------------------------------------------------------------ Global Chaos Synchronization of Two different Chaotic Systems Using Nonlinear Control Israr Ahmad a*, Azizan Bin Saaban b , Adyda Binti Ibrahim c , Mohammad Shehzad d a School of Quantitative Sciences, College of Arts & Sciences, UUM, Malaysia, College of Applied Sciences Nizwa, Ministry of Higher Education, Sultanate of Oman. b, c School of Quantitative Sciences, College of Arts & Sciences, UUM, Malaysia d College of Applied Sciences Nizwa, Ministry of Higher Education, Sultanate of Oman. a iak_2000plus@yahoo.com b azizan@uum.edu.my c adyda@uum.edu.my d shehzad.niz@cas.edu.om, Abstract Synchronization between two chaotic systems occurs when the trajectory of one of the system asymptotically follows the trajectory of another system due to coupling or due to forcing. In this research paper, the synchronization problem between two identical Li and identical Lorenz systems and nonidentical Li and Lorenz Chaotic Systems have been addressed. In this study, the synchronization is performed through a nonlinear controller based on Lyapuonov Stability Theory to stabilize the error dynamics. It has been shown that the proposed strategies have excellent transient performances using less control effort with fast transient speed and has shown analytically as well as graphically that synchronization is asymptotically globally stable. Numerical simulations are carried out to verify and support the analytical results of the proposed methodology by using mathematica 9. Keywords: Synchronization, Nonlinear Active Control, Lyapunov Stability Theory, Lorenz & Li Chaotic Systems. 1. Introduction The Synchronization of Chaos is one way of explaining sensitive dependence on initial conditions which is known as the Butterfly Effect [1]. ------------------------------------------------------------ *Corresponding author. E-mail address: iak_2000plus@yahoo.com 225