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| | Hello from Germany. I'm glad to came here. My first name is Jaqueline. <br>I live in a city called Saarlouis in western Germany.<br>I was also born in Saarlouis 21 years ago. Married in March year 2012. I'm working at the college.<br><br>my web site; [http://nordicprogress.com/foxy/index.php?do=/blog/1058/fifa-coin-generator/ Fifa 15 Coin generator] |
| [[Image:DuffingMap.png|right|thumb|Plot of the Duffing map showing chaotic behavior, where ''a'' = 2.75 and ''b'' = 0.15.]]
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| [[Image:Tw duffing.png|right|thumb|[[Phase portrait]] of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior.]]
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| 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
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| :<math>x_{n+1}=y_n\,</math> | |
| :<math>y_{n+1}=-bx_n+ay_n-y_n^3.\,</math>
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| 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]].
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| ==References==
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| {{reflist}}
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| == External links ==
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| * [http://scholarpedia.org/article/Duffing_oscillator Duffing oscillator on Scholarpedia]
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| {{Chaos theory}}
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| [[Category:Chaotic maps]]
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| {{Mathapplied-stub}}
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Latest revision as of 07:19, 4 September 2014
Hello from Germany. I'm glad to came here. My first name is Jaqueline.
I live in a city called Saarlouis in western Germany.
I was also born in Saarlouis 21 years ago. Married in March year 2012. I'm working at the college.
my web site; Fifa 15 Coin generator