  The stability analysis of self-similar solutions is an important approach to
confirm whether they act as an attractor in general non-self-similar
gravitational collapse. Assuming that the collapsing matter is a perfect fluid
with the equation of state $P=\alpha\rho$, we study spherically symmetric
non-self-similar perturbations in homogeneous self-similar collapse described
by the flat Friedmann solution. In the low pressure approximation $\alpha \ll
1$, we analytically derive an infinite set of the normal modes and their growth
(or decay) rate. The existence of one unstable normal mode is found to conclude
that the self-similar behavior in homogeneous collapse of a sufficiently low
pressure perfect fluid must terminate and a certain inhomogeneous density
profile can develop with the lapse of time.
