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attractor, we represent in Figure 5 the projection of the trajectory 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 , on the x$_{2}$ − y$_{2}$ − z$_{2}$ space. The simulation result confirms that system (5 . 11) + (5 . 14) + (5 . 17) possesses a chaotic attractor. 

## 6 Control of Tori 

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In this section, we will numerically demonstrate the stabilization of the unstable quasi-periodic motions embedded in the chaotic attractor of the unidirectionally coupled Duffing oscillators (5 . 11) + (5 . 14) + (5 . 17) . We suppose that to stabilize the quasi-periodic solutions of (5.14) and (5.17) it is sufficient to control the chaos of system (5.11). For that purpose we will make use of the Ott-Grebogi-Yorke (OGY) control method [9] applied to the logistic map (5.10), which gives rise to the presence of chaos in (5.11). We proceed by briefly explaining the OGY control method for the map [69]. 

Suppose that the parameter λ in the logistic map (5.10) is allowed to vary in the range [3 . 9 − ε, 3 . 9+ ε ] , where ε is a given small number. Consider an arbitrary solution { κ$_{i}$ } , κ$_{0}$ ∈ [0 , 1] , of the map and denote by κ ( j $^{)}$, j = 1 , 2 , . . . , p, the target unstable p − periodic orbit to be stabilized. In the OGY control method [69], at each iteration step i after the control mechanism is switched on, we consider the map (5.10) with the parameter value λ = ¯ λ$_{i}$, where 

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provided that the number on the right-hand side of the formula (6 . 18) belongs to the interval [3 . 9 − ε, 3 . 9+ ε ] . In other words, we apply a perturbation in the amount of 3 . 9[2 κ ( j ) − 1][ κ$_{i}$ − κ ( j $^{)}$] κ ( j $^{)}$[1 − κ ( j $^{)}$] to the parameter 

