Response of Complex Systems to Complex Perturbations: Complexity Matching

Abstract

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