Chaos Lab

Discrete map · 1D · dim 1

Tent map

Piecewise-linear cousin of the logistic map with the same topological structure but no quadratic curvature. The full tent (μ = 2) is conjugate to the logistic at r = 4 and to the Bernoulli shift on binary strings.

Bifurcation diagram of the tent map across μ ∈ [1, 2]. Above μ = 1 the orbit is chaotic everywhere.

Equations

x_{n+1} = μ · min(x_n, 1 − x_n)

At a glance

Parametersμ ∈ (1, 2]
Chaotic forμ > 1
Lyapunov exponentλ = ln μ
HistoryStudied extensively from the 1970s onward.

Try it

Open the interactive playground at /tools/cobweb.

See also

Quick quiz

Test yourself on tent

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

  1. Q1.The Lyapunov exponent of the tent map x ↦ μ·min(x, 1−x) is:

  2. Q2.At μ = 2 the tent map is conjugate to the:

  3. Q3.Below μ = 1 the tent map has:

  4. Q4.Compared to logistic, the tent has:

  5. Q5.The tent map has an invariant density equal to:

  6. Q6.The skew tent map differs from the symmetric tent by:

  7. Q7.Topological entropy of the full tent map is:

  8. Q8.Tent map's bifurcation diagram differs from logistic in:

0 of 8 answered