On the other hand, according to the Pyragas control method [27, 43], an unstable periodic solution with period τ$_{0}$ can be stabilized by using an external perturbation of the form C [ s ( t − τ$_{0}$ ) − s ( t )] , where C is the strength of the perturbation, s ( t ) is a scalar signal which is given by some function of the state of the system and s ( t − τ$_{0}$ ) is the signal measured with a time delay equal to τ$_{0}$. To stabilize an unstable quasi-periodic solution of (4.26), we construct the following control system, We make use of the OGY control method around the fixed point 2 . 9 / 3 . $_{9}$of the logistic map (4.22) so that ¯ λ$_{j}$ in (4.28) is given by the formula (4.27) in which κ ( i ) ≡ 2 . 9 / 3 . $_{9}$. The control mechanism is switched on 18 Figure 5: The stabilized quasi-periodic solution of system (4.26). Figure 4: Chaos control of system (4.26). We make use of the OGY control method around the fixed point 2 . 9 / 3 . $_{9}$of the logistic map (4.22). The control is switched on at t = ζ$_{70}$. The OGY control switched off at t = ζ$_{350}$, while the Pyragas control is switched off at t = ζ$_{400}$. The values ε = 0 . 085 and C = 2 . 6 are used in the simulation. 0 50 100 150 200 250 300 350 400 450 500 −2 0 2 t w 3 0 50 100 150 200 250 300 350 400 450 500 −6 −4 −2 0 2 t w 4 200 205 210 215 220 225 230 235 240 245 250 0.8 1 1.2 1.4 t w 3 200 205 210 215 220 225 230 235 240 245 250 −1.2 −1 −0.8 t w 4 w ′ 1 = w$_{2}$ w ′ 2 = − 1 . 4 w$_{1}$ − 0 . 82 w$_{2}$ − 0 . 01 w 3 1 + v ( t, ζ, ¯ λ$_{j}$ ) w ′ 3 = w$_{4}$ + 1 . 2( w$_{1}$ + 0 . 1 sin( w$_{1}$ )) w ′ 4 = − 0 . 15 w$_{4}$ + 0 . 5 w$_{3}$ (1 − w 2 $_{3}$) + 0 . 4 arctan( w$_{2}$ ) +0 . 2 sin(0 . 9 w$_{5}$ ) + C [ w$_{4}$ ( t − 2 π/ 0 . 9) − w$_{4}$ ( t )] w ′ 5 = 1 . (4.28)