Discrete map · 1D · dim 1
Sine map
Topologically equivalent to the logistic in the chaotic regime; the smoothness changes critical exponents in transient analysis. Common in studies of period-doubling universality.
Equations
x_{n+1} = a · sin(π x_n)At a glance
| Parameters | a ∈ (0, 1] |
|---|---|
| Chaotic for | a close to 1 (a > a∞ ≈ 0.86) |
| Lyapunov exponent | varies with a |
| History | Feigenbaum's universality calculations used this map as a smoothness check. |
Try it
Open the interactive playground at /tools/cobweb.