Two Coupled Logistic Maps
J. C. Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706,
January 14, 1997
Shown here is a system of two coupled logistic maps described by the equations
= (1 - eps) A1 xn (1 - xn)
+ eps A2 yn (1 - yn)
= (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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