The attractor is the subset of the
domain, which attracts a set of initial condition in the limit.
A strange attractor is simply the pattern of the pathway, in visual form, produced by graphing the behavior of a system. Since many, if not most, nonlinear systems are unpredictable and yet patterned, it is called strange and since it tends to produce a fractal geometric shape, it is said to be attracted to that shape, IKEDA is one of those systems.
Like the logistic map the Ikeda system is a system with
a discrete time scale n=1, 2, ...(i. e. it is a map). Whereas the logistic
map maps a one-dimensional real interval [0..1]onto itself, the Ikeda map
is defined on the two-dimensional real plane. And whereas there is only
one control parameter r in the logistic map, there are four control parameters
b, l and r
in the Ikeda map.
To illustrate this ideas, we consider
the Ikeda map which we write as:
it can also be written as:
y(n+1)=b(x(n).sin(t)+y(n).cos(t)) where: t=l-r/(1+x(n)²+y(n)²)