Metastability due to a branching-merging structure in a simple network of an exclusion process

TL;DR

This paper studies how a simple network with branching and merging causes metastability in particle flow, revealing critical points and phases that depend on boundary conditions, with implications across various network systems.

Contribution

It analytically characterizes metastability and tipping points in a branching-merging network using the exclusion process, a novel insight into such structures.

Findings

Metastability occurs in both periodic and open boundary conditions.

Two types of metastability identified: hysteresis and nonergodic phase.

Critical conditions for metastability collapse are analytically derived.

Abstract

We investigate a simple network, which has a branching-merging structure, using the totally asymmetric simple exclusion process, considering conflicts at the merging point. For both periodic and open boundary conditions, the system exhibits metastability. Specifically, for open boundary conditions, we observe two types of metastability: hysteresis and a nonergodic phase. We analytically determine the tipping points, that is, the critical conditions under which a small disturbance can lead to the collapse of metastability. Our findings provide novel insights into metastability induced by branching-merging structures, which exist in all network systems in various fields.