Control and synchronization of hyperchaotic states in mathematical models of Bènard-Marangoni convective experiments

Mathematical models are of great interest for experimentalists since they provide a way for controlling and synchronizing different chaotic states. In previous works, we have used a Takens-Bogdanov (T-B) system under hyperchaotic dynamic conditions (two or more positive Lyapunov exponents) because they adequately reflect the dynamics of the patterns in small aspect ratio pre-turbulent Bènard-Marangoni convection near a codimension-2 point (with resonance between 2:1 modes), in square symmetry (D4). In this paper, we discuss the coupling of two different four dimensional hyperchaotic models derived from the Lorenz equations by using the same method introduced in previous works. As in the former system of used equations, we found that two identical hyperchaotic systems based on either Chen or Lü equation systems evolve into different states in the pattern space, where the synchronization state or the complexity could be controlled by a small external signal, as was shown in T-B equations.