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

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.