  The dynamical emergence (and subsequent intermittent breakdown) of collective
behavior in complex systems is described as a non-Poisson renewal process,
characterized by a waiting-time distribution density $\psi (\tau)$ for the time
intervals between successively recorded breakdowns. In the intermittent case
$\psi (t)\sim t^{-\mu}$, with complexity index $\mu $. We show that two systems
can exchange information through complexity matching and present theoretical
and numerical calculations describing a system with complexity index $\mu_{S}$
perturbed by a signal with complexity index $\mu_{P}$. The analysis focuses on
the non-ergodic (non-stationary) case $\mu \leq 2$ showing that for
$\mu_{S}\geq \mu_{P}$, the system $S$ statistically inherits the correlation
function of the perturbation $P$. The condition $\mu_{P}=\mu_{S}$ is a resonant
maximum for correlation information exchange.
