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.