Table 3.

Mathematical models of the chaotic maps [45].

No	Name	Chaotic map	Range
1	Chebyshev	$x_{i+1}=\cos (i\times {\cos }^{-1}(x_i))$	(-1,1)
2	Gauss/mouse	$x_{i+1}=\{\begin{array}{cc}1& x_i=0\\ \frac{1}{\mathrm{mod}(x_i,1)}& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$	(0,1)
3	Singer	$x_{i+1}=\mu \times (7.86\times x_i-23.31\times x_i^2+28.75\times x_i^3-13.302875\times x_i^4),\begin{array}{c}\\ \mu =1.07\end{array}$	(0,1)
4	Bernoulli	$x_{i+1}=2\times x_i(mod\text{1})$	(0,1)
5	Sine	$x_{i+1}=\frac{a}{4}\times \sin (\pi \times x_i),a=4$	(0,1)
6	Circle	$x_{i+1}=\mathrm{mod}(x_i+b-(\frac{a}{2\times \pi })\times sin(2\times \pi \times x_k),1),\text{b}=\text{0}\text{.2 and a}=\text{0}\text{.5}$	(0,1)