Global Chaos Synchronization of Rucklidge Chaotic Systems for Double Convection via Sliding Mode Control

In the recent decades, there is great interest shown in the literature in the finding of chaotic motion and oscillations in nonlinear dynamical systems arising in physics, chemistry, biology, and engineering. Chaotic systems have many important applications in science and engineering. This paper discusses the Rucklidge chaotic system (1992) for nonlinear double convection. When the convection takes place in a fluid layer rotating uniformly about a vertical axis and in the limit of tall thin rolls, convection in an imposed vertical magnetic field and convection in a rotating fluid layer are both modeled by Rucklidge’s third-order set of ordinary differential equations which produces chaotic solutions. This paper starts with a detailed analysis of the Rucklidge’s nonlinear double convection system and the parameter values for which the Rucklidge system exhibits chaotic behaviour. Next, a sliding mode control law is devised for the global chaos synchronization of the Rucklidge chaotic systems. The main results for the chaos synchronization of Rucklidge chaotic systems are established using Lyapunov stability theory. Next, the sliding mode control results are illustrated with numerical simulations using MATLAB.