#
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
*x*_{n}_{+1}
= (1 - *eps*) *A*_{1 }*x*_{n }(1 - *x*_{n})
+ *eps A*_{2 }*y*_{n }(1 - *y*_{n})
*y*_{n}_{+1}
= (1 - *eps*) *A*_{2 }y_{n }(1 - *y*_{n})
+ *eps A*_{1 }*x*_{n }(1 - *x*_{n})
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 *A*_{1}*A*_{2}
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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