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Noise-induced multistability in chemical systems: Discrete versus continuum modeling

Andrew Duncan1, Shuohao Liao1, Tomáš Vejchodský1,2, Radek Erban1,*, and Ramon Grima3,†

  • 1Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
  • 2Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-115 67, Czech Republic
  • 3School of Biological Sciences, Kings Buildings, Mayfield Road, University of Edinburgh, EH9 3JF, United Kingdom

  • *erban@maths.ox.ac.uk
  • †ramon.grima@ed.ac.uk
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Phys. Rev. E 91, 042111 – Published 10 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042111

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. It has recently been shown that for a particular system, the CFPE captures noise-induced multistability predicted by the CME. This phenomenon involves the CME's marginal probability distribution changing from unimodal to multimodal as the system size decreases below a critical value. We here show that the CFPE does not always capture noise-induced multistability. In particular we find simple chemical systems for which the CME predicts noise-induced multistability, whereas the CFPE predicts monostability for all system sizes.

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Phys. Rev. E 91, 042111– Published 10 April, 2015
  • Received 28 July 2014

©2015 American Physical Society

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