A Novel Double Convection Chaotic System, Its Analysis, Adaptive Control and Synchronization

In this research work, we announce a novel 3-D double convection chaotic system and discuss its qualitative properties, adaptive control and synchronization. First, this work describes the dynamic equations and qualitative properties of the novel 3-D double convection chaotic system. We show that the novel 3-D double convection chaotic system has three unstable equilibrium points of which one equilibrium point is a saddle-point and the other two equilibrium points are saddle-foci. Our novel chaotic system is obtained by modifying the equations of the Rucklidge chaotic system (1992) for nonlinear double convection. The Lyapunov exponents of the novel 3-D double convection chaotic system are obtained as \(L_1 = 1.03405, L_2 = 0\) and \(L_3 = -4.03938\). Also, the Kaplan-Yorke dimension of the novel 3-D double convection chaotic system is derived as \(D_{KY} = 2.2560\). Next, this work describes the global stabilization of the novel 3-D double convection chaotic system with unknown parameters via adaptive control method. Furthermore, this work describes the global chaos synchronization of identical novel 3-D double convection chaotic systems via adaptive control method. Our adaptive global stabilization and synchronization results are established via Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this work for the novel 3-D double convection chaotic system.