Figure 4: The behavior of the V coordinate of system (2.20) is shown in (a). In (b) and (c), where the chaotic behavior is observable, the amplitudes are restricted to the ranges 15 − 16 . 6 and 7 . 4 − 8 . 6 , respectively. Making use of the solution U ( τ ) whose graph is represented in Figure 10 in both of the systems (2.20) and (2.21), we depict in Figure 6 the projection of the stroboscopic plot of system (2.20)-(2.21) on the V − W plane. The first 500 iterations are omitted in the simulation. The time interval [0 , 80 × 10 $^{6}$] is used and the time step is taken as Δ τ = 5000 . Since the plot does not take place on the line W = V , we conclude that generalized synchronization is not achieved in the dynamics of the coupled system (2.19)-(2.20). with the boundary conditions We introduce the auxiliary system ρ (0 , τ ) = 0 , σ ( L, τ ) = γµρ ( L, τ ) , φ (0 , τ ) = 0 , φ ( L, τ ) = −W . ∂$_{τ}$ σ − ∂$_{z}$ ( E σ ) = σ E α ( E ) , ∂$_{τ}$ ρ + µ∂$_{z}$ ( E ρ = σ E α E , ∂$_{z}$ E = ˜ ρ − σ, E = − ∂$_{z}$φ, ∂$_{τ}$ W = 17 . 7 − W − R$_{s}$ j + 0 . 047 U ( τ ) τ$_{s}$ (2.21) 2.5 3 3.5 4 x 10 6 6 8 10 12 14 16 18 time V a 2.5 3 3.5 4 x 10 6 15 16 time V b 2.5 3 3.5 4 x 10 6 7.5 8 8.5 time V c 11