Transition Phenomena Induced by Internal Noise and Quasi-absorbing State

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.

6 pages, 5 figures

References in corpus (9)

• Shift in the velocity of a front due to a cut-off
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• The Importance of Being Discrete - Life Always Wins on the Surface
• Transitions Induced by the Discreteness of Molecules in a Small Autocatalytic System
• Spectral theory of metastability and extinction in a branching-annihilation reaction
• Adaptation of Autocatalytic Fluctuations to Diffusive Noise
• Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics
• Alteration of Chemical Concentrations through Discreteness-Induced Transitions in Small Autocatalytic Systems
• "Quantum phase transitions" in classical nonequilibrium processes

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