Chaos Lab

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.

Bifurcation diagram of the Gauss map x ↦ exp(−6.2 x²) + β; quasi-periodic route to chaos.

Equations

x_{n+1} = exp(−α x_n²) + β

At a glance

Parametersα, β ∈ ℝ (typical α ≈ 6.2, β ∈ [−1, 1])
Chaotic forvarious parameter windows; see bifurcation diagram
HistoryInvestigated in the late 1970s as a test bed for universal scaling.

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See also

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