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An Example of Two-Dimensional Chaos

​
map parameters
a
1.42
b
2.25
initial condition: {
x
0
,
y
0
}
number of iterations
100
250
500
1000
2000
color scheme
background color
point size
6
x
k
This Demonstration illustrates the behavior of the two-dimensional map
x
k+1
=(a
x
k
+b
y
k
)(1-a
x
k
-b
y
k
)
,
y
k+1
=
x
k
. Depending on the choices of parameters and initial condition, the behavior may be periodic or chaotic. For some choices of parameters, this behavior is sensitive to small changes in the initial condition.
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