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2 - Deterministic versus Stochastic Modelling

Published online by Cambridge University Press:  04 November 2019

Radek Erban  and
S. Jonathan Chapman
Radek Erban
Affiliation:
University of Oxford
S. Jonathan Chapman
Affiliation:
University of Oxford
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Summary

This chapter presents examples of chemical systems where deterministic modelling fails and a stochastic approach is necessary. They include a chemical system with stochastic switching between favourable states of a system, and systems close to the bifurcation points of the corresponding deterministic ordinary differential equation (ODE) models. It is shown that the stochastic model might have qualitatively different properties than its deterministic counterpart for some parameter regimes. A chemical reaction system can also be redesigned, by adding extra reactions, in such a way that its stochastic behaviour qualitatively changes, while its deterministic ODEs do not change at all. In particular, there exist many stochastic reaction networks that correspond to the same deterministic ODE model.

Keywords

stochastic switchingstochastic focusingstochastic oscillationsstochastic resonancemultistable systemsnoise-induced oscillationssynthetic biology
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Chapter
Information
Stochastic Modelling of Reaction–Diffusion Processes , pp. 33 - 58
Publisher: Cambridge University Press
Print publication year: 2020

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