The chaos control techniques such as the Pyragas and OGY methods are suitable for either continuous- time or discrete-time systems [48, 50, 80, 81]. However, to the best of our knowledge, there is no chaos control technique for dynamics on time scales. This is the main reason why we apply the Pyragas control to the logistic map in order to control the chaos of (5.10). It is worth noting that the OGY algorithm can also be applied to the logistic map to control the chaos of (5.10). Now, let us describe the Pyragas control technique for the logistic map (5.11). The aim in this method is to stabilize the unstable fixed point 1 − 1 /µ of (5.11) by using the delayed feedback control algorithm where β is the feedback gain [48, 49, 51]. According to the results of the paper [49], the nonzero fixed point becomes stable for µ − 3 2 < β < 1 , and the optimal value of the feedback gain, which leads to the fastest convergence of nearby initial conditions is β$_{op}$ = µ − 2( µ − 1) 1 / $^{2}$. It was mentioned in [49] that the algorithm (6.12) is successful if the initial data are sufficiently close to the fixed point, and solutions of (6.12) can escape to infinity for some initial data from the chaotic attractor of (5.11). In order to guarantee the stabilization for any initial data, Pyragas and Pyragas [49] proposed that the condition has to be satisfied for a suitably chosen small positive number ε, which can be determined only numeri- cally. The inequality (6.13) is used to estimate the strength of the perturbation β ( ζ$_{k}$ − ζ$_{k}$$_{−}$$_{1}$ ) if it would be applied at a given iteration step k. On the other hand, the condition is required to avoid the stabilization of the zero fixed point [49]. In the Pyragas control method, at each iteration step k after the control mechanism is switched on, we consider the map (6.12) with a chosen value of β between ( µ − 3) / 2 and 1 provided that (6.13) and (6.14) are valid. Otherwise, we take β = 0 and wait until both (6.13) and (6.14) are satisfied. 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 that depends on the ergodic properties of (5.11) before the fixed point is stabilized. Now, we will apply the Pyragas control technique to the logistic map (5.11) with µ = 3 . 9 around the fixed point 2 . 9 / 3 . 9 to control the chaos of (5.10). For that purpose, we take into account the following 16 ζ$_{k}$$_{−}$$_{1}$ > µ − 1 − [(1 − µ ) 2 − 4 µε ] 1 / 2 2 µ (6.14) | ζ$_{k}$ − ζ$_{k}$$_{−}$$_{1}$ | < ε (6.13) ζ$_{k}$$_{+1}$ = µζ$_{k}$ (1 − ζ$_{k}$ ) + β ( ζ$_{k}$ − ζ$_{k}$$_{−}$$_{1}$ ) , (6.12)