Continuum limit for interacting systems on adaptive networks

TL;DR

This paper proves that large systems of interacting particles on adaptive networks can be approximated by a continuum limit, with well-posedness established, using graph convergence techniques.

Contribution

It introduces a rigorous framework for deriving continuum limits of adaptive network systems and proves their well-posedness.

Findings

Large systems can be approximated by continuum models

Continuum models are mathematically well-posed

Graph convergence is key to the approximation

Abstract

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large systems the dynamics can be approximated by the corresponding continuum limit. Well-posedness of the latter is also established.