−4 −2 0 2 4 200 210 220 230 240 250 260 270 y$_{1}$ y 3 Figure 5: The trajectory of the response system (2.3) with r = 99 . 51 . Chaotic behavior is observable in the figure. the chaos of the response. We make use of conditional Lyapunov exponents [9] and the auxiliary system approach [12] to show the absence of GS in the investigated systems. It is worth noting that the results are valid for both identical and non-identical systems, i.e., the coefficients of the coupled Lorenz systems can be same or different. One of the concepts related to our results is the global unpredictable behavior of the weather dynamics. This subject was considered in [19] on the basis of Lorenz systems assuming that the whole atmosphere of the Earth is partitioned in a finite number of subregions such that in each of them the dynamics of the weather is governed by the Lorenz system with certain coefficients. The present paper plays a complementary role to the discussions of [19] in such a way that the unpredictable behavior of the weather dynamics is permanent under the interaction of two subregions whose dynamics are both governed by chaotic Lorenz systems. Another concept in which Lorenz systems are encountered is the laser dynamics. It was shown by Haken [25] that the Lorenz model is identical with that of the single mode laser. Therefore, our results may also be used as an engineering tool to design unsynchronized chaotic Lorenz lasers [26]. The proof of Theorem 3.1 is as follows. Proof. Fix an arbitrary positive number δ$_{1}$, a point y$_{0}$ ∈ U , and a chaotic solution x ( t ) of (2.1). One can find ϵ$_{0}$ > 0 and Δ > 0 such that for arbitrary δ$_{0}$ > 0 both of the inequalities ‖ x (0) − x (0) ‖ < δ$_{0}$ and ‖ x ( t ) − x ( t ) ‖ > ϵ$_{0}$, t ∈ J, hold for some chaotic solution x ( t ) of (2.1) and for some interval J ⊂ [0 , ∞ ) , whose length is not less than Δ . Take an arbitrary y$_{1}$ ∈ U such that ‖ y$_{0}$ − y$_{1}$ ‖ < δ$_{1}$. For the sake of brevity, let us denote y ( t ) = φ$_{x}$$_{(}$$_{t}$$_{)}$ ( t, y$_{0}$ ) and y ( t ) = φ$_{x}$$_{(}$$_{t}$$_{)}$ ( t, y$_{1}$ ) . It is worth noting that there exist positive numbers K$_{0}$ and H$_{0}$ such that ‖ y ( t ) ‖ , ‖ y ( t ) ‖ ≤ K$_{0}$ for all t ≥ 0 , and sup t ≥ 0 ‖ x ( t ) ‖ ≤ H$_{0}$ for each chaotic solution x ( t ) of (2.1). 9 Appendix: Proof of Theorem 3.1