__Ikeda attractor__

Let's start by looking at the attracator (with the specify
parameter below)

a=1 b=0.9
l=0.4
r=6

we remark that b=1 is a special case for which the dynamic system is conservative.

Chaotic Attractors of the Ikeda Map

a=1 b=0.65 l=0.4 r=6
a=1 b=0.75
l=0.4
r=6

a=1 b=0.8 l=0.4 r=6
a=1 b=0.9
l=0.4
r=6

We can remark that, gradualy by increasing the value
of b
from 0.65 to 0.9, we
have a chaotic behavior of the Ikeda map as we can see above.

Then when b is greater than 0.9 we obtain a new behavior, it appears a convergence point as we can see in the figure below.

__The basin of attraction__

Points in blue iterarte to a fixed point, points in yellow to a chaotic attractor, and in red we have the attractor.