ϵ, 3 . 8 + ϵ ] . In other words, we apply a perturbation in the amount of 3 . 8(2 κ ( q ) − 1)( κ$_{j}$ − κ ( q $^{)}$) κ ( q $^{)}$(1 − κ ( q $^{)}$) to the parameter µ = 3 . 8 of the logistic map, if the trajectory { κ$_{j}$ } is sufficiently close to the target peri- odic orbit. This perturbation makes the map behave regularly so that at each iteration step the orbit κ$_{j}$ is forced to be located in a small neighborhood of a previously chosen periodic orbit κ ( q $^{)}$. Unless the parameter perturbation is applied, the orbit κ$_{j}$ moves away from κ ( q ) due to the instability. If ∣ ∣$^{3}$$^{.}$$^{8(2}$$^{κ}$$^{(}$$^{jq}$$^{)}$ − 1)( κ$_{j}$ − κ ( q $^{)}$) κ ( q $^{)}$(1 − κ ( q $^{)}$) ∣ $_{> ε}$, we set ¯ µ$_{j}$ = 3 . 8 , so that the system evolves at its original parameter value, and wait until the trajectory { κ$_{j}$ } enters a sufficiently small neighborhood of the periodic orbit κ ( q $^{)}$, q = 1 , 2 , . . . , p, such that the inequality − ϵ ≤ 3 . 8(2 κ ( q ) − 1)( κ$_{j}$ − κ ( q $^{)}$) κ ( q $^{)}$(1 − κ ( q $^{)}$) ≤ ϵ holds. If this is the case, the control of chaos is not achieved immediately after switching on the control mechanism. Instead, there is a transition time before the desired periodic orbit is stabilized. The transition time increases if the number ϵ decreases [39]. The chaos of system A$_{2}$ can be stabilized by controlling an unstable periodic orbit of the logistic map A$_{1}$, since the map gives rise to the presence of chaos in the system. By applying the OGY control method around the fixed point 2 . 8 / 3 . 8 of the logistic map, we stabilize the corresponding unstable 2 − periodic solution of system A$_{2}$. The simulation result is seen in Figure 7. We used the same initial data as in Figure 2. It is seen in Figure 7 that the OGY control method successfully controls the chaos of system A$_{2}$. The control is switched on at t = θ$_{50}$ and switched off at t = θ$_{280}$. The values κ$_{0}$ = 0 . 63 and ϵ = 0 . 08 are utilized in the simulation. The control becomes dominant approximately at t = 150 and its effect lasts approximately until t = 340 , after which the instability becomes dominant and irregular behavior develops again. Next, we will demonstrate the stabilization of an unstable quasi-periodic solution of system A$_{3}$. We suppose that an unstable quasi-periodic solution of A$_{3}$ can be stabilized by controlling the chaos of system $_{A$_{2}$}$. We use the solution shown in Figure 7 as the perturbation in system A$_{3}$, and represent in Figure 8 the solution of A$_{3}$ with y$_{2}$ ( t$_{0}$ ) = 0 . 95 , k$_{2}$ ( t$_{0}$ ) = 0 . 38 , where t$_{0}$ = 0 . 63 . Similarly to system A$_{2}$, it seen in the figure that the chaos of A$_{3}$ is controlled approximately for 150 ≤ t ≤ 340 . To reveal that the stabilized solution is indeed quasi-periodic, we depict in Figure 9 the graph of the same solution for 200 ≤ t ≤ 300 . Figure 9 manifests that application of the OGY control method Figure 7: The chaos control of system A$_{2}$. The OGY control method is applied around the fixed point 2 . 8 / 3 . 8 of the logistic map. The value ϵ = 0 . 08 is used. 0 50 100 150 200 250 300 350 400 450 500 0.08 0.12 0.16 t y 1 15