Adaptive control of a two-scroll novel chaotic system with a quartic nonlinearity

This paper proposes a two-scroll novel 3-D chaotic system with a quartic nonlinearity and devises an adaptive control law for globally stabilizing the system when the system parameters are unknown. First, this paper derives fundamental qualitative properties of the new chaotic system such as dissipativity, symmetry, invariance, Lyapunov exponents and Lyapunov dimension. The phase portraits of the novel chaotic system are shown using MATLAB. Next, this paper uses adaptive control theory and Lyapunov stability theory to derive an adaptive feedback control law for globally stabilizing the novel chaotic system for all initial conditions. The main result is proved with the help of Lyapunov stability theory. Adaptive control results are validated by MATLAB simulations.