  A generic model of stochastic autocatalytic dynamics with many degrees of
freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time
evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) =
\lambda w_i(t)$ at the individual level with a global coupling through a
constraint which does not allow the $w_i$'s to fall below a lower cutoff given
by $c \cdot \bar w$, where $\bar w$ is their momentary average and $0<c<1$ is a
constant. The dynamic variables $w_i$ are found to exhibit a power-law
distribution of the form $p(w) \sim w^{-1-\alpha}$. The exponent $\alpha (c,N)$
is quite insensitive to the distribution $\Pi(\lambda)$ of the random factor
$\lambda$, but it is non-universal, and increases monotonically as a function
of $c$. The "thermodynamic" limit, N goes to infty and the limit of decoupled
free multiplicative random walks c goes to 0, do not commute: $\alpha(0,N) = 0$
for any finite $N$ while $ \alpha(c,\infty) \ge 1$ (which is the common range
in empirical systems) for any positive $c$. The time evolution of ${\bar w (t)}
$ exhibits intermittent fluctuations parametrized by a (truncated)
L\'evy-stable distribution $L_{\alpha}(r)$ with the same index $\alpha$. This
non-trivial relation between the distribution of the $w_i$'s at a given time
and the temporal fluctuations of their average is examined and its relevance to
empirical systems is discussed.
