Two Coupled Logistic Maps

J. C. Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706, USA
January 14, 1997

 
Shown here is a system of two coupled logistic maps described by the equations
 
xn+1 = (1 - eps) A1 xn (1 - xn) + eps A2 yn (1 - yn)
 
yn+1 = (1 - eps) A2 yn (1 - yn) + eps A1 xn (1 - xn)
 
where eps is the coupling constant.  For eps = 0, the two maps are decoupled, and for eps = 1, they are fully cross-coupled, meaning that the output of one map is the input to the other and vice versa.  The animation below shows the region in A1A2 space (3 < A < 4) for which chaos occurs as eps varies from 0 to 1.  The top number in the upper left of the image is eps, and the lower number is the percent of the region that is chaotic.
 
 
The (PowerBASIC) source and (DOS) object code that produced the above image are available for download.

 


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