is chaotic, and it will be accompanied by the boundary conditions We will take into account (2.19) as the drive system. The solutions of (2.19) will be used as a perturbation for the response GDS system in the form, with the boundary conditions In system (2.20), δ is a nonzero number and the term δ U ( τ ) /τ$_{s}$ is the perturbation from the drive system (2.19). It is shown in the Appendix for the parameter value U$_{t}$ = 17 . 7 that the projection of the attractor of system (1.16)-(1.18) on the domain of equation (1.18) is a stable limit cycle (see Fig. 8). That is, in the absence of driving, the response system (2.20) with V$_{t}$ = 17 . 7 does not possess chaos. We will numerically show that the response GDS system possesses chaotic motions near the limit cycle, provided that the driving effect is included. Our results are theoretically based on the study [1], where we have proved that if the drive system admits infinitely many unstable periodic solutions and sensitivity, then the response system does the same. Since the attractor exists in system (1.16)-(1.18) with U$_{t}$ = 17 . $_{7}$, one can conclude by the extension of our results presented in [1] that if the number | δ | in equation (2.20) is sufficiently small, then system (2.20) possesses cyclic chaos. That is, entrainment by chaos takes place in the system. Let us take V$_{t}$ = 17 . 7 and δ = 0 . 047 in the response GDS system (2.20). Using the solution of the drive system shown in Figures 9, 10 and 11, we depict in Figure 2 the projection of a chaotic solution of (2.20) on the V − ˜ j plane. On the other hand, the projection of the stroboscopic plot of the response system on the same plane is shown in Figure 3. Both of the figures reveal that the response GDS system 9 ˜ ρ (0 , τ ) = 0 , σ ( L, τ ) = $^{γµ}$˜ ρ ( L, τ ) , ˜ φ (0 , τ ) = 0 , ˜ φ ( L, τ ) = −V . ∂$_{τ}$ ˜ σ − ∂$_{z}$ ( ˜ $^{E}$˜ σ ) = ˜ σ ˜ E α ( ˜ E ) , ∂$_{τ}$ ρ + µ∂$_{z}$ ρ = σ E α E , ∂$_{z}$ ˜ E = ˜ ρ − ˜ σ, ˜ E = − ∂$_{z}$ ˜ φ, ∂$_{τ}$ V = V$_{t}$ − V − R$_{s}$ ˜ j + δ U ( τ ) τ$_{s}$ , (2.20) ρ (0 , τ ) = 0 , σ ( L, τ ) = γµρ ( L, τ ) , φ (0 , τ ) = 0 , φ ( L, τ ) = −U .