Analysis and Anti-Synchronization of a Novel Chaotic System via Active and Adaptive Controllers

Anti-synchronization of chaotic systems deals with the problem of asymptotically synchronizing the sum of states of a pair of chaotic systems called master and slave systems with the help of controllers attached to the slave system. When two chaotic systems are anti-synchronized, then their states are asymptotically equal in magnitude, but opposite in phase. Anti-synchronization of chaotic systems has applications in many engineering areas such as secure communications, secure data encryption, cryptosystems, etc. This paper announces a novel 3-D chaotic system and describes its qualitative properties. Next, this paper deals with the design of active and adaptive controllers for synchronizing the states of identical novel chaotic systems. Active controllers are used when the system parameters are available for measurement and the synchronization result is established using Lyapunov stability theory. Adaptive controllers are used when the system parameters are unknown. In this case, estimates are used in lieu of the unknown system parameters and adaptive controllers are designed using adaptive control theory and Lyapunov stability theory. Numerical simulations using MATLAB have been shown to demonstrate the proposed active and adaptive synchronization results for novel chaotic systems.