Plot of the Duffing map showing chaotic behavior, where *a* = 2.75 and *b* = 0.15.

Phase portrait 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.

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This page was last edited on 15 July 2017, at 14:38