λ = 3 . 9 of the logistic map, if the trajectory { κ$_{i}$ } is sufficiently close to the target periodic orbit. This perturbation makes the map behave regularly so that at each iteration step the orbit κ$_{i}$ is forced to be located in a small neighborhood of a previously chosen periodic orbit κ ( j $^{)}$. Unless the parameter perturba- tion is applied, the orbit κ$_{i}$ moves away from κ ( j ) due to the instability. If ∣ ∣$^{3}$$^{.}$$^{9[2}$$^{κ}$$^{(}$$^{j}$$^{)}$ − 1][ κ$_{i}$ − κ ( j $^{)}$] κ ( j $^{)}$[1 − κ ( j $^{)}$] ∣ > ε , we set ¯ λ$_{i}$ = 3 . 9 , so that the system evolves at its original parameter value, and wait until the trajectory { κ$_{i}$ } enters a sufficiently small neighborhood of the periodic orbit κ ( j $^{)}$, j = 1 , 2 , . . . , p, such that the in- equality − ε ≤ 3 . 9[2 κ ( j ) − 1][ κ$_{i}$ − κ ( j $^{)}$] κ ( j $^{)}$[1 − κ ( j $^{)}$] ≤ 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 [54]. An unstable 2 − periodic solution of (5.11) can be stabilized by controlling the 1 − periodic orbit of the logistic map (5.10), i.e. the fixed point 2 . 9 / 3 . 9 of the map. We apply the OGY control method around the fixed point of the logistic map to stabilize the corresponding quasi-periodic solution of the 6 − dimensional system (5 . 11) + (5 . 14) + (5 . 17) . Figure 6 represents the x$_{2}$, y$_{2}$ and z$_{2}$ coordinates of (5 . 11) + (5 . 14) + (5 . 17) corresponding to the initial data x$_{1}$ ( t$_{0}$ ) = 0 . 24 , x$_{2}$ ( t$_{0}$ ) = 0 . 16 , y$_{1}$ ( t$_{0}$ ) = 1 . 32 , y$_{2}$ ( t$_{0}$ ) = − 2 . 25 , z$_{1}$ ( t$_{0}$ ) = 0 . 37 , z$_{2}$ ( t$_{0}$ ) = − 3 . 71 , where t$_{0}$ = 0 . 61 . The control mechanism is switched on at t = θ$_{35}$ and switched off at t = θ$_{95}$. The value ε = 0 . 06 is used in the simulation. There is a transition time such that the control becomes dominant approximately at t = 53 , and it prolongs approximately till t = 148 , after which chaos develops again. It is seen in Figure 6 that the 2 − periodic solution of system (5.11) is controlled for 53 ≤ t ≤ 148 , and accordingly the corresponding quasi-periodic solutions of systems (5.14) and (5.17) are stabilized in the same interval of time. Moreover, we illustrate the stabilized torus of system (5 . 11) + (5 . 14) + (5 . 17) in Figure 7. Both of the Figures 6 and 7 support the result of Theorem 4.1 such that they manifest the presence of quasi-periodic motions embedded in the chaotic attractor of (5 . 11) + (5 . 14) + (5 . 17) . The possibility of replacing infinitely many periodic solutions by more general types of regular motions in a chaotic attractor was considered in the studies [7, 8, 43]. The present paper provides a method to obtain chaotic attractors with infinitely many almost periodic motions instead of periodic ones. In this way, the complexity of chaos increases. Chaos in the sense of Li-Yorke and the one obtained through a cascade of almost periodic motions are considered in the present study. One of the advantages of the proposed procedure is the controlla- bility of the obtained chaos. A control technique for stabilizing the unstable almost periodic motions is presented, and control of tori is numerically demonstrated by means of the OGY control method [9] in unidirectionally coupled Duffing oscillators. The results reveal that the OGY control method is suitable 7 Conclusions 15