Observation and inverse problems in coupled cell networks

TL;DR

This paper studies how to infer the overall behavior of coupled cell networks from observations of a single cell, demonstrating that such observation properties are generally valid for most interaction functions.

Contribution

It establishes that, for almost all interaction functions, observing a single cell suffices to deduce the network's global dynamics.

Findings

Observation properties hold for almost all interactions

Single-cell observation can reveal network behavior

Results apply to various network dynamics

Abstract

A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism, economical networks... It consists in a directed graph $G$, each node (or cell) representing an agent of the network and each directed arrow representing which agent acts on which one. It yields a system of differential equations $\dot x(t)=f(x(t))$, where the component $i$ of $f$ depends only on the cells $x_j(t)$ for which the arrow $j\rightarrow i$ exists in $G$. In this paper, we investigate the observation problems in coupled cell networks: can one deduce the behaviour of the whole network (oscillations, stabilisation etc.) by observing only one of the cells? We show that the natural observation properties holds for almost all the interactions $f$.