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

Hiroki Yamamoto, Daichi Yanagisawa, Katsuhiro Nishinari
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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.
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排除过程的简单网络中分支-合并结构的亚稳态
研究了一个具有分支-合并结构的简单网络,在考虑合并点冲突的情况下,采用完全不对称的简单排除过程。在周期边界和开边界条件下,系统都表现出亚稳态。具体来说,对于开放边界条件,我们观察到两种类型的亚稳态:滞后和非遍历相位。我们分析地确定了临界点,即小的扰动可以导致亚稳态崩溃的临界条件。我们的发现对分支-合并结构引起的亚稳态提供了新的见解,这种亚稳态存在于各个领域的所有网络系统中。
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