Chaos Lab

Discrete map · 2D · dim 2

Duffing map (discrete)

Discrete analogue of the Duffing oscillator. Produces chaos for a window of parameters; useful for studying noise-driven escape from a double well.

Discrete Duffing map at (a, b) = (2.75, 0.2).

Equations

x_{n+1} = y_n
y_{n+1} = −b x_n + a y_n − y_n³

At a glance

Parametersa, b ∈ ℝ (classic: a = 2.75, b = 0.2)
Chaotic fora ≈ 2.75, b ≈ 0.2
HistoryInspired by Duffing's 1918 nonlinear oscillator equation.

See also

Quick quiz

Test yourself on duffing-map

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

  1. Q1.The discrete Duffing map is related to:

  2. Q2.Its equations are:

  3. Q3.Classical chaotic parameters are:

  4. Q4.Compared to its continuous-time parent, the discrete map:

  5. Q5.The cubic term y³ in the iteration:

  6. Q6.The discrete Duffing map is:

  7. Q7.Iterating from (0, 0) gives:

  8. Q8.The continuous Duffing oscillator from which this map descends has how many parameters?

0 of 8 answered