We argue that complex systems, defined as non-Poisson renewal process, with complexity index $\mu$, exchange information through complexity matching. We illustrate this property with detailed theoretical and numerical calculations describing a system with complexity index $\mu_{ S}$ perturbed by a signal with complexity index $\mu_{ P}$. We focus our attention on the case $1.5 \leq \mu_S \leq 2$ and $1 \leq \mu_{ P} \leq 2$. We show that for $\mu_{ S} \geq \mu_P$, the system S reproduces the perturbation, and the response intensity increases with increasing $\mu_P$. The maximum intensity is realized by the matching condition $\mu_P = \mu_S$. For $\mu_{ P} > \mu_{ S}$ the response intensity dies out as $1/t^{ \mu_P-\mu_S}$.
Categories: cond-mat.stat-mech