Duffing map

{{Short description|Discrete-time dynamical system}}

{{no footnotes|date=June 2013}}

Image:DuffingMap.png

Image:Tw duffing.png of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior.]]

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 (x_n, y_n) in the plane and maps it to a new point given by

:$x\_\{n+1\}=y\_n$

:$y\_\{n+1\}=-bx\_n+ay\_n-y\_n^3.$

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.