The Duffing 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
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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“Unless, governor, teacher inspector, visitor,
This map becomes their window and these windows
That open on their lives like crouching tombs
Break, O break open,”
—Stephen Spender (1909–1995)