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Nonlinear Coupled Oscillator

​
parameters
(a, b)
2D slider
a
0.6
b
0.6
plot range
x
min
-2.
x
max
2
y
min
-2.2
y
max
1.6
steps and axes
steps
40000
axes
Initialization timed out
This Demonstration plots the points (
x
n+1
,
y
n+1
), where
x
n+1
=a
y
n
+b-
2
x
n
and
y
n+1
=a
x
n
+b-
2
y
n
for
n>50
​
, starting with
x
0
=
-7
10
and
y
0
=2
-7
10
. With different parameters
a
and
b
you will get similar pictures. Start with only 1000 steps and then choose an appropriate number of steps and an adequate plot range. You will get other interesting pictures, for example, with the parameters (0.31, 0.884), (0.456, 0.83), (0.49, 0.717), (0.564, 0.594), and (-0.612, 0.872).
The recurrence equations constitute a two-parameter
(a,b)
canonical form of a nonlinear coupled oscillator.
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