Table 1 The utilized chaotic maps. The range of all maps is (0,1).
Name | Chaotic map |
|---|---|
Gauss/mouse | \({x_{i+1}}=\left\{ \begin{gathered} 1{\text{ }}{x_i}=0 \hfill \\ {1 \mathord{\left/ {\vphantom {1 {\bmod ({x_i},1)}}} \right. \kern-0pt} {\bmod ({x_i},1)}}{\text{ otherwise}} \hfill \\ \end{gathered} \right.\) |
Quadratic | \({x_{i+1}}={x^2}_{i} - 1{\text{ }}\) |
Singer | \({x_{i+1}}=1.07 \times (7.86 \times {x_i} - 23.31 \times {x_i}^{2}+28.75 \times {x_i}^{3} - 13.3 \times {x_i}^{4})\) |
Logistic | \({x_{i+1}}=4{x_i} \times (1 - {x_i})\) |
Tent | \({x_{i+1}}=\left\{ \begin{gathered} {\text{1}}{\text{0.43}} \times {x_i}{\text{ }}{x_i}<0.7 \hfill \\ 3.33 \times (1 - {x_i}){\text{ }}{x_i} \geqslant {\text{0}}{\text{0.7}} \hfill \\ \end{gathered} \right.{\text{ }}\) |
Bernoulli | \({x_{i+1}}=2 \times {x_i}(mod{\text{ 1}})\) |
