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We investigate a simple network, which has a branching-merging structure,using the totally asymmetric simple exclusion process, considering conflicts atthe merging point. For both periodic and open boundary conditions, the systemexhibits metastability. Specifically, for open boundary conditions, we observetwo types of metastability: hysteresis and a nonergodic phase. We analyticallydetermine the tipping points, that is, the critical conditions under which asmall disturbance can lead to the collapse of metastability. Our findingsprovide novel insights into metastability induced by branching-mergingstructures, which exist in all network systems in various fields.

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