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On the Fractional Order Generalized Discrete Maps Chapter | 13 383
FIGURE 13.4 (A) General bifurcation diagram of the generalized logistic map and 3D snap-
shots (B) at b 5 1 and a 5 f0:5; 1; 2g and (C) at a 5 1 and b 5 f0:5; 1; 2g.
scaling map” because only the vertical axis is affected by the parameter b,
while the map with b 5 1 is called “zooming map” because both axes are
affected by the parameter a. These effects can be further inferred from the
three-dimensional snapshots of bifurcation diagrams against the main system
parameter λ for different values of the scaling parameters a and b, which are
shown in Fig. 13.4B and C, respectively.
13.2.2.2 Generalized Tent Map With Scaling Parameters
Similarly, the generalized tent map with scaling parameters (Sayed et al.,
2015a) is given by:
8 a
μ x; x #
>
b 1 1
>
<
fðxÞ 5 a : ð13:4Þ
μða 2 bxÞ; x .
>
b 1 1
>
:
