Response of Complex Systems to Complex Perturbations: Complexity Matching

Abstract

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 $1.5\le {\mu }_S\le 2$ and $1\le {\mu }_P\le 2$. We show that for ${\mu }_S\ge {\mu }_P$, 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 $1/t^{{\mu }_P-{\mu }_S}$.

4 pages, 3 figures, submitted to prl