Table 1 Comparison of chaotic region.
Map expression | Parameter values | Chaotic region |
|---|---|---|
\({x_{n+1}}=r{x_n}\left( {1 - {x_n}} \right)\) | / | \(r \in [3.57,4.00]\) |
\({x_{n+1}}=rx_{n}^{\alpha }\left( {1 - x_{n}^{\alpha }} \right)\) | \(\alpha =1.1\) | \(r \in [3.66,4.00]\) |
\({x_{n+1}}={x_n}\exp \left( {r\left( {1 - {x_n}} \right)} \right)\) | / | \(r \in [2.69,7.62]\) |
\({x_{n+1}}=r{x_n}{\left( {1 - {x_n}} \right)^{ - b}}\) | \(b= - 2.0\) | \(r \in [5.31,9.00]\) |
\(r=5.0\) | \(b \in [ - 1.79, - 1.37]\) | |
\({x_{n+1}}=\alpha {x_n}{r^{1 - {x_n}}}\) | \(\alpha =2.0\) | \(r>7.35\) |
\(r=1.5\) | \(\alpha>9.87\) |
