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.

Try it

Open the interactive playground at /tools/cobweb.

See also

Quick quiz

Test yourself on gauss

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.The Gauss / mouse map exhibits which route to chaos as β varies?

  2. Q2.The Gauss map is defined by:

  3. Q3.Why is it sometimes called the 'mouse map'?

  4. Q4.Compared to the logistic map, the Gauss map shows:

  5. Q5.Distinct from Carl-Friedrich Gauss's continued-fraction Gauss map?

  6. Q6.Iterating the Gauss map at α = 6.2, β = −0.5 gives:

  7. Q7.The Gauss map is bounded because:

  8. Q8.Gauss-map chaos is used as a model of:

0 of 8 answered