Duffing equation (strange attractor)
This simulation explores the Duffing equation, which reads (in
dimensionless variables) as follows:
x'' + 2 γ x' - x
(1-x2) = f cos ωt
where each '
denotes a time derivative.
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You can select below the parameters γ and f, as
well as the initial conditions for the elongation x and the
velocity v = x'.
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The unit time is 1/ ω (so that ω = 1).
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Since the equation is not autonomous, the full phase space is that of
triplets (t, x, v) or, since t only
appears in the cosinus, (ωt mod 2π, x, v).
The simulation will display a projection of the orbit in a space in
which the phase ωt mod 2π coils around an axis.
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The simulation will also display 3 stroboscopic Poincaré sections
defined by the conditions ωt mod 2π = φ, φ+2/3π,
φ+4/3π.
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The point of view of the three-dimensional projections can be changed
with the cursors or the mouse.
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Each whole image can be moved with the mouse while pressing Ctrl.
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To change the zoom in the projections, press Shift
when moving up or down the mouse pointer.
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Put the mouse pointer over an element to get information about it.