Kaplan–Yorke map
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The Kaplan–Yorke map is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Kaplan–Yorke map takes a point (xn, yn ) in the plane and maps it to a new point given by
where mod is the modulo operator with real arguments. The map depends on only the one constant α.
Calculation method
Due to roundoff error, successive applications of the modulo operator will yield zero after some ten or twenty iterations when implemented as a floating point operation on a computer. It is better to implement the following equivalent algorithm:
where the and
are computational integers. It is also best to choose
to be a large prime number in order to get many different values of
.
References
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- Lua error in package.lua at line 80: module 'strict' not found.
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