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

TL;DR

This paper investigates how complex systems exchange information through a phenomenon called complexity matching, where systems with similar complexity indices synchronize their behavior, especially in non-ergodic regimes, revealing a resonance condition for optimal information transfer.

Contribution

The study introduces a theoretical and numerical framework for understanding complexity matching in non-ergodic systems, highlighting the resonance condition when complexity indices are equal.

Findings

Systems with higher complexity index inherit the correlation functions of perturbations.

Maximum information exchange occurs when the complexity indices of system and perturbation match.

The analysis focuses on non-ergodic regimes with complexity index μ ≤ 2.

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 $\mu \leq 2$ 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.