Projective vector field: Difference between revisions
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[[Image:DuffingMap.png|right|thumb|Plot of the Duffing map showing chaotic behavior, where ''a'' = 2.75 and ''b'' = 0.15.]] | |||
[[Image:Tw duffing.png|right|thumb|[[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 [[chaos theory|chaotic behavior]]. The Duffing [[function (mathematics)|map]] takes a point (''x<sub>n</sub>'', ''y<sub>n</sub>'') in the [[plane (mathematics)|plane]] and maps it to a new point given by | |||
:<math>x_{n+1}=y_n\,</math> | |||
:<math>y_{n+1}=-bx_n+ay_n-y_n^3.\,</math> | |||
The map depends on the two [[constant (mathematics)|constant]]s ''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]]. | |||
==References== | |||
{{reflist}} | |||
== External links == | |||
* [http://scholarpedia.org/article/Duffing_oscillator Duffing oscillator on Scholarpedia] | |||
{{Chaos theory}} | |||
[[Category:Chaotic maps]] | |||
{{Mathapplied-stub}} | |||
Revision as of 22:07, 18 May 2013
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
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.
References
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