y$_{1}$ − y$_{2}$ − y$_{3}$ space. In Figure 1, the projection of the trajectory corresponding to the initial data x$_{1}$ (0) = − 8 . 631 , x$_{2}$ (0) = − 2 . 382 , x$_{3}$ (0) = 33 . 096 , y$_{1}$ (0) = 10 . 871 , y$_{2}$ (0) = − 4 . 558 , y$_{3}$ (0) = 70 . 541 is shown in blue, and the one corresponding to the initial data x$_{1}$ (0) = − 8 . 615 , x$_{2}$ (0) = − 2 . 464 , x$_{3}$ (0) = 33 . 067 , y$_{1}$ (0) = 10 . 869 , y$_{2}$ (0) = − 4 . 561 , y$_{3}$ (0) = 70 . 537 is shown in red. The time interval [0 , 2 . 96] is used in the simulation. One can observe in Figure 1 that even if the trajectories in blue and red are initially nearby, later they diverge, and this behavior supports the result of Theorem 3.1 such that sensitivity is present in the dynamics of (2.3). In other words, the figure confirms that sensitivity is a permanent feature of (2.2) even if it is perturbed with the solutions of (2.1). Figure 1: Sensitivity in the response system (2.3). The simulation supports the result of Theorem 3.1 such that sensitivity is permanent in system (2.2) although it is driven by the solutions of (2.1). On the other hand, in Figure 2, we represent the trajectory of (2.3) corresponding to x$_{1}$ (0) = 4 . 43 , x$_{2}$ (0) = − 2 . 27 , x$_{3}$ (0) = 30 . 81 , y$_{1}$ (0) = 3 . 09 , y$_{2}$ (0) = 4 . 98 , y$_{3}$ (0) = 46 . 21 . It is seen in Figure 2 that the trajectory is chaotic, and this reveals the persistence of chaos in the dynamics of (2.3). GS [10] is said to occur in the coupled system (2 . 1) + (2 . 3) if there exist sets X , Y ⊂ R 3 of initial conditions and a transformation ψ defined on the chaotic attractor of (2.1) such that for all x$_{0}$ ∈ X , y$_{0}$ ∈ Y the relation lim t →∞ ‖ y ( t ) − ψ ( x ( t )) ‖ = 0 holds, where x ( t ) and y ( t ) are respectively the solutions of (2.1) and (2.3) satisfying x (0) = x$_{0}$ and y (0) = y$_{0}$. If GS occurs, a motion that starts on X × Y collapses onto a manifold M ⊂ X × Y of synchronized motions. The transformation ψ is not required to exist for the transient trajectories. When ψ is the identity transformation, the identical synchronization takes place [9]. It was formulated by Kocarev and Parlitz [11] that the systems (2.1) and (2.3) are synchronized in the generalized sense if and only if for all x$_{0}$ ∈ X , y$_{0}$, y$_{0}$ ∈ Y , the asymptotic stability criterion lim t →∞ ‖ y ( t, x$_{0}$, y$_{0}$ ) − y ( t, x$_{0}$, y$_{0}$ ) ‖ = 0 , 5 −20 −10 0 10 20 −40 −20 0 20 40 40 50 60 70 80 90 y$_{2}$ y$_{1}$ y 3