Let's start by looking at the attracator (with the specify
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=0.8 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.