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in the coupled system (5.12)+(5.17) with ζ , and consider the following control system conjugate to (5.12)+(5.17): 

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Figure 5 represents the time series of the w$_{3}$ − coordinate of the control system (6.20) corresponding to the initial data ζ$_{0}$ = 0 . 56 , w$_{1}$ ( t$_{0}$ ) = 0 . 24 , w$_{2}$ ( t$_{0}$ ) = 0 . 17 , w$_{3}$ ( t$_{0}$ ) = 0 . 43 , w$_{4}$ ( t$_{0}$ ) = 0 . 04 , where t$_{0}$ = 0 . 56 . The OGY algorithm is applied around the fixed point 2 . 9 / 3 . 9 of the logistic map (1.5) by setting κ ( j ) ≡ 2 . 9 / 3 . 9 in equation (6.18). The control is switched on at t = ζ$_{50}$ and switched off at t = ζ$_{400}$, i.e., we take µ$_{i}$ = 3 . 9 for 0 ≤ i < 50 and i ≥ 400 in (6.19). Moreover, the value ε = 0 . 08 is used in the simulation. One can observe in Figure 5 that one of the quasi-periodic solutions embedded in the chaotic attractor of (5.17) is stabilized. A transient time occurs after the control is switched on such that the stabilization becomes dominant approximately at t = 124 and prolongs approximately till t = 477 after which the chaotic behavior develops again. Moreover, the stabilized quasi-periodic solution of (5.17) is represented in Figure 6. Figures 5 and 6 manifest that the proposed numerical technique, which is based on the OGY algorithm, is appropriate to control the chaos of system (5.17). 

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