The Duffing equation (or Duffing oscillator), named after Georg Duffing, is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by

where the (unknown) function x=x(t) is the displacement at time t, is the first derivative of x with respect to time, i.e. velocity, and is the second time-derivative of x, i.e. acceleration. The numbers , , , and are given constants.