Duffing equation
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' (x and v can also be
selected by moving with the mouse the point on the display Phase
space).
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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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It is possible to draw the x(t) evolution, the phase
space, any stroboscopic Poincaré section (defined by a condition in
the form ωt mod 2π = φ) and the evolution
of the mechanical energy (when f = 0, one gets with the latter
the graph of the potential energy in red).