Discrete map · 1D · dim 1
Gauss (mouse) map
Sometimes called the 'mouse map' for its characteristic shape. Exhibits a rich variety of bifurcations as β varies, including a quasi-periodic route to chaos.
Equations
x_{n+1} = exp(−α x_n²) + βAt a glance
| Parameters | α, β ∈ ℝ (typical α ≈ 6.2, β ∈ [−1, 1]) |
|---|---|
| Chaotic for | various parameter windows; see bifurcation diagram |
| History | Investigated in the late 1970s as a test bed for universal scaling. |
Try it
Open the interactive playground at /tools/cobweb.