Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity

In this research work, an eight-term 3-D novel chaotic system with an exponential nonlinearity has been derived. The basic qualitative properties of the 3-D chaotic system have been discussed in detail. The new chaotic system has only one equilibrium point, which is a saddle-point. Hence, the system has an unstable equilibrium. The Lyapunov exponents of the 3-D chaotic system are obtained as L1 = 14.0893, L2 = 0 and L3 = -33.9828. Since the maximal Lyapunov exponent of the novel chaotic system is L1 = 14.0893, which is a large value, the novel chaotic system has strong chaotic behaviour. The Lyapunov dimension of the chaotic system is obtained as DL = 2.4146. Next, an adaptive control law has been designed to stabilise the unstable chaotic system with unknown system parameters. The adaptive control result has been established using Lyapunov stability theory. MATLAB simulations have been shown in detail to illustrate the phase portraits and adaptive control results for the novel chaotic system.