w ′ 1 = w$_{2}$, w ′ 2 = − 4 w$_{1}$ − 1 . 5 w$_{2}$ − 0 . 02 w 3 1 + cos t + ν$_{1}$ ( t, ζ ) , w ′ 3 = w$_{4}$ + 0 . 7 w 2 1 − 1 . 2 w$_{1}$, w ′ 4 = − 2 . 5 w$_{3}$ − 3 . 5 w$_{4}$ + 0 . 01 w 3 − 1 . 5 cos( πt ) + ν$_{2}$ ( t, ζ ) + arctan( w$_{2}$ ) . (6.20) in the coupled system (5.12)+(5.17) with ζ , and consider the following control system conjugate to (5.12)+(5.17): 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). Figure 5: Control of the chaos of (5.17) by means of the OGY method applied to the map (1.5) around its fixed point 2 . 9 / 3 . 9 . The value ε = 0 . 08 is used, and the control is switched on at t = ζ$_{50}$ and switched off at t = ζ$_{400}$. Figure 6: The stabilized quasi-periodic solution of (5.17). 0 100 200 300 400 500 600 −0.5 0 0.5 t w 3 13 220 240 260 280 300 320 340 360 380 400 −0.6 −0.4 −0.2 0 0.2 t w 3