The behaviour of the system in this zone is no more "absolute" but can only be interpreted in terms of probability.

The graph below shows the evolution of the system for
r_{1}=1.25 and r_{2}=0.81:

What is plotted is the logarithm of the n^{th}
iterate versus n.

We can see that the system still diverges to infinity
but the main difference with the previous case is that the growth of X(n)
is no more monotonic: as the ratio r_{2} is smaller than 1, the
system does not always move away from the origin.

Actually, when the center B_{1} is choosen, the
system effectively tends to diverge but at the opposite, when the center
B_{2} is choosen, the iterates tends to get closer to the origin.

The final system is the result of the competition between theses two effects.

It is important to notice that the probabilities p_{1}
and p_{2} play a large role in the behaviour of the system in this
domain.

Actually, the ratio r_{2} can be very small (and
hence B_{2} be very attractive) but if the probability of the associated
function is not large enough, the system will still diverge.

What happends is that after a great number N of iterations,
the first function is chosen N*p_{1} times and the second function
is chosen N*p_{2} times.

Moreover, if | X(n) | is great compared to D=(B_{2}-B_{1}),
we can roughly say that | X(n+1) | ~ | r | * | X(n) | with r=r_{1}
or r_{2}.

Thus, after N iterations and in average, we have | X(N)
| ~ | r_{1} |^{Np1} * | r_{2} |^{Np2 }*
| X(0) |.

Consequently, if R = | r_{1} |^{p1} *
| r_{2} |^{p2} is greater than one the system diverges
with a probability equal to one.

At the opposite, if R is smaller than one the system
diverges with a probability equal to zero (see next page).

Conclusion:

This case corresponds to R>1, and so, even if the system
does not diverge in an absolute way, the probabilty to diverge is equal
to one and we can say that there is still no attractor.