| I only know a little - Duffings equation is a nonlinear second order
equation with a sinusoidal forcing function; Duffing wrote a monograph
on this at the turn of the century. It can be written as a pair of
coupled equations - this may be why you refered to them as plaural.
Very little is really known about the solutions - as is usual for
nonlinear equations, but there are some of the usual tricks - like
perturbing a linear equation and so on. You may want to look at the
following books, and then just do some numerical experiments...
Try
Introduction to Nonlinear Differential and Integral Equations
H. T. Davis, Dover
Nonlinear Oscillations
P. Hagedorn, Oxford
Both are mathematical and have a reasonable discussion of Duffings
and other equations. Davis' book in particular has a lot of interesting
material that is hard to find - use of elliptic functions, asymptotic
expansions, and so forth.
- Jim
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