Adaptive synchronization of two-scroll novel chaotic systems with a quartic nonlinearity

Synchronization of different types, control and regulation of chaotic systems are important areas of research in the control literature and various methods have been adopted for these research problems. Also, the discovery of novel chaotic systems in various applications, their qualitative properties and the control of such systems are also important research areas in chaos theory. This paper proposes a novel 3-D chaotic system and details its qualitative properties such as Lyapunov exponents and Lyapunov dimension. Next, the main result of this paper, namely, an adaptive feedback controller has been constructed for the drive-response synchronization of novel systems for all initial states when the system parameters are unknown. Phase orbits of the new chaotic system have been demonstrated using numerical simulations with MATLAB. Adaptive feedback results for the drive-response synchronization of the systems have been also illustrated using numerical simulations with MATLAB.