Kaplan–Yorke map

A plot of 100,000 iterations of the Kaplan-Yorke map with α=0.2. The initial value (x0,y0) was (128873/350377,0.667751).

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 .


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