Bifurcation Diagram of the Hénon Map

parameters

α Minimum: 0.91

α Maximum: 1.41

β: 0.3035

number of iterates

n

125

250

500

number of α values

m

500

750

1000

magnification

1

2

4

10

20

The Hénon map is the two-dimensional map described by the equations

x

k+1

=-α

x

k

x

k

+

y

k

+1

,

y

k+1

=β

x

k

.

The plot shows the last 36

x

coordinates after

n

iterations of the Hénon map using the initial point

(-0.1,0.0)

.

To obtain an interesting region of periodic and chaotic behavior, we use

m

α

values between 0.91 and 1.41 with

β=0.3035

. Changing these values will give very similar results.

You can click anywhere in the diagram to see a magnified inset in the lower-left corner.