Consider the following Lorenz system [3] where σ , r , and b are constants. System (2.1) has a rich dynamics such that for different values of the parameters σ, r and b, the system can exhibit stable periodic orbits, homoclinic explosions, period-doubling bifurcations, and chaotic attractors [21]. In the remaining parts of the paper, we suppose that the dynamics of (2.1) is chaotic, i.e., the system admits sensitivity and infinitely many unstable periodic motions embedded in the chaotic attractor. In this case, (2.1) possesses a compact invariant set Λ ⊂ R $^{3}$. Next, we take into account another Lorenz system, where x ( t ) = ( x$_{1}$ ( t ) , x$_{2}$ ( t ) , x$_{3}$ ( t )) is a solution of (2.1) and g ( x ) = ( g$_{1}$ ( x ) , g$_{2}$ ( x ) , g$_{3}$ ( x )) is a continuous function such that there exists a positive number L$_{g}$ satisfying ‖ g ( x ) − g ( x ) ‖ ≥ L$_{g}$ ‖ x − x ‖ for all x, x ∈ Λ . Here, ‖ . ‖ denotes the usual Euclidean norm in R $^{3}$. It is worth noting that the coupled system (2 . 1)+ (2 . 3) has a skew product structure. We refer to (2.1) and (2.3) as the drive and response systems, respectively. In the next section, we will demonstrate the existence of sensitivity in the dynamics of the response system. 3 where the parameters σ, r and b are such that system (2.2) is also chaotic. Systems (2.1) and (2.2) are, in general, non-identical, since the coefficients σ, r, b and σ, r, b can be different. We perturb (2.2) with the solutions of (2.1) to set up the system ˙ y$_{1}$ = − σy$_{1}$ + σy$_{2}$ + g$_{1}$ ( x ( t )) ˙ y$_{2}$ = − y$_{1}$y$_{3}$ + ry$_{1}$ − y$_{2}$ + g$_{2}$ ( x ( t )) ˙ y$_{3}$ = y$_{1}$y$_{2}$ − by$_{3}$ + g$_{3}$ ( x ( t )) , (2.3) ˙ u$_{1}$ = − σu$_{1}$ + σu$_{2}$ ˙ u$_{2}$ = − u$_{1}$u$_{3}$ + ru$_{1}$ − u$_{2}$ ˙ u$_{3}$ = u$_{1}$u$_{2}$ − bu$_{3}$, (2.2) ˙ x$_{1}$ = − σx$_{1}$ + σx$_{2}$ ˙ x$_{2}$ = − x$_{1}$x$_{3}$ + rx$_{1}$ − x$_{2}$ ˙ x$_{3}$ = x$_{1}$x$_{2}$ − bx$_{3}$, (2.1) 2 The model