Abstract
In this work, we announce an eleven-term novel 4-D hyperchaotic thermal convection system with two quadratic nonlinearities. The phase portraits of the novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel 4-D hyperchaotic thermal convection system is obtained by introducing a feedback control to the 3-D thermal convection system obtained by Wang et al. (J Fluid Mech 237: 479-498, 1992). The Lyapunov exponents of the novel hyperchaotic thermal convection system are obtained as L-1 = 0.40546, L-2 = 0.03583, L-3 = 0 and L-4 = -6.44038. Since there are two positive Lyapunov exponents for the novel 4-D thermal convection system, it is hyperchaotic. The Maximal Lyapunov Exponent (MLE) of the novel hyperchaotic system is found as L-1 = 0.40546. Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is derived as D-KY = 3.0685. Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic thermal convection system with unknown parameters. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical novel hyperchaotic thermal convection systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work.