What exactly is Duffing's equation, and how does the strange attractor associated with it emerge?

The Duffing oscillator is a second-order oscillator with constant
damping, a nonlinear restoring force expressed as a low order
polynomial, and a sinusoidal time-periodic forcing.  The behavior of
this equation was studied by Georg Duffing in his book Erzwungene
Schwingungen bei Veraenderlicher Eigenfrequenz, published in 1917.  Any
good book on nonlinear oscillations is likely to mention this equation.

Chaotic attractors in Duffing's oscillator were first described by
Yoshisuke Ueda, a student of Chihiro Hayashi, in 1973 in a paper in the
Trans. IECE Japan Vol. 56a, pp. 218-225.  A paper by Ueda which appeared
in P.J. Holmes (ed.), New Approaches to Nonlinear Problems in Dynamics,
published by SIAM in 1980, contains a wealth of information about
chaotic regimes.  Holmes has written a number of articles on the Duffing
oscillator.  Further references can be found in J.M.T. Thompson and
H.B. Stewart, Nonlinear Dynamics and Chaos, published by John Wiley, and
in J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical
Systems, and Bifurcations of Vector Fields published by Springer Verlag.

A beginner's introduction to the geometric theory of nonlinear
oscillations can be found in R. Abraham and C. Shaw, Dynamics: the
Geometry of Behavior, published by Aerial Press.

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