Duffing equation (Baker transformation)
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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For information on other elements, put over them the mouse pointer to
get a tooltip.
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The simulation will display N2 stroboscopic Poincaré
sections defined by a series of conditions in the form
ωt
mod 2π = φ + 2 n π/N2
for
n = 0, 1, …, N2-1 (from left to right
and then from top to bottom)