Long-range interactions and disorder facilitate pattern formation in spatial complex systems

TL;DR

This paper derives stability criteria for spatial complex systems with local and non-local interactions, showing how long-range interactions and disorder can induce pattern formation, with non-reciprocity suppressing instabilities.

Contribution

It introduces a coarse-grained field theory framework to analyze stability in biological-like systems with noise and non-local interactions, highlighting the role of long-range interactions and non-reciprocity.

Findings

Long-range interactions lead to pattern formation.

Disorder and noise influence stability and fluctuations.

Non-reciprocity suppresses certain instabilities.

Abstract

Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and non-locality may affect stability. Here, we derive stability criteria for spatial complex systems with local and non-local interactions from a coarse-grained field theory with multiplicative noise. We show that long-range interactions give rise to a transition between regimes exhibiting giant density fluctuations and pattern formation. This instability is suppressed by non-reciprocity in interactions.