Noise-induced multistability in chemical systems: Discrete vs Continuum modeling

Abstract

The noisy dynamics of chemical systems is commonly studied using either the chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE). The latter is a continuum approximation of the discrete CME approach. We here show that the CFPE may fail to capture the CME's prediction of noise-induced multistability. In particular we find a simple chemical system for which the CME's marginal probability distribution changes from unimodal to multimodal as the system-size decreases below a critical value, while the CFPE's marginal probability distribution is unimodal for all physically meaningful system sizes.

arXiv comment5 pages, 2 figures

References in corpus (5)

• Analytical distributions for stochastic gene expression
• Noise-Induced Bistable States and Their Mean Switching Time in Foraging Colonies
• Steady-state fluctuations of a genetic feedback loop: an exact solution
• How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
• The complex chemical Langevin equation

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