The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Duffing map takes a point (xn, yn) in the plane and maps it to a new point given by
x n + 1 = y n {\displaystyle x_{n+1}=y_{n}}
y n + 1 = − b x n + a y n − y n 3 . {\displaystyle y_{n+1}=-bx_{n}+ay_{n}-y_{n}^{3}.}
The map depends on the two constants a and b. These are usually set to a = 2.75 and b = 0.2 to produce chaotic behaviour. It is a discrete version of the Duffing equation.
External links Duffing oscillator on Scholarpedia