Transition Phenomena Induced by Internal Noise and Quasi-absorbing State

TL;DR

This paper investigates how internal noise influences transition phenomena in a simple chemical reaction system, highlighting the role of quasi-absorbing states in causing bifurcations in stationary distributions.

Contribution

It introduces a simplified model to analyze transition phenomena driven by internal noise and elucidates the critical role of quasi-absorbing states in these transitions.

Findings

Quasi-absorbing states are crucial in transition phenomena.

Internal noise strength affects the stability of quasi-absorbing states.

Discontinuous bifurcation occurs in stationary probability distributions.

Abstract

We study a simple chemical reaction system and effects of the internal noise. The chemical reaction system causes the same transition phenomenon discussed by Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72 (2003) 62]. By using the simpler model than Togashi-Kaneko's one, we discuss the transition phenomenon by means of a random walk model and an effective model. The discussion makes it clear that quasi-absorbing states, which are produced by the change of the strength of the internal noise, play an important role in the transition phenomenon. Stabilizing the quasi-absorbing states causes bifurcation of the peaks in the stationary probability distribution discontinuously.