Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

Abstract

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 $\mu \le 2$ showing that for ${\mu }_S\ge {\mu }_P$, 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.

4 pages, 1 figure