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

First, this paper announces a five-term novel 3-D conservative chaotic system with a quadratic nonlinearity and a sextic nonlinearity. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. The Lyapunov exponents of the novel conservative chaotic system are obtained as L 1 = 0.0846, L 2 = 0 and L 3 = –0.0846. Since the sum of the Lyapunov exponents is zero, the 3-D novel chaotic system is conservative. The maximal Lyapunov exponent (MLE) for the novel chaotic system is obtained as L 1 = 0.0846 and Lyapunov dimension as D L = 3. Next, an adaptive controller is designed to achieve generalized projective synchronization (GPS) of two identical novel conservative chaotic systems with unknown system parameters. MATLAB simulations have been shown to demonstrate the phase portraits of the conservative system and the GPS results derived via the adaptive control method.