  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.
