A 3-D Novel Conservative Chaotic System and its Generalized Projective Synchronization via Adaptive Control

Abstract

This research work proposes a five-term 3-D novel conservative chaotic system with a quadratic nonlinearity and a quartic nonlinearity. The conservative chaotic systems have the important property that they are volume conserving. The Lyapunov exponents of the 3-D novel chaotic system are obtained as �! = 0.0836, �! = 0 and �! = −0.0836. Since the sum of the Lyapunov exponents is zero, the 3-D novel chaotic system is conservative. Thus, the Kaplan-Yorke dimension of the 3-D novel chaotic system is easily seen as 3.0000. The phase portraits of the novel chaotic system simulated using MATLAB depict the chaotic attractor of the novel system. This research work also discusses other qualitative properties of the system. Next, an adaptive controller is designed to achieve Generalized Projective Synchronization (GPS) of two identical novel chaotic systems with unknown system parameters. MATLAB simulations are shown to validate and demonstrate the GPS results derived in this work.

Keywords

• Chaos
• chaotic systems
• conservative systems
• synchronization
• generalized projective synchronization
• adaptive control.