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1 results

  • 2 - Deterministic versus Stochastic Modelling

  • Radek Erban, University of Oxford, S. Jonathan Chapman, University of Oxford
  • Book:
    Stochastic Modelling of Reaction–Diffusion Processes
    Published online:
    04 November 2019
    Print publication:
    30 January 2020, pp 33-58

  • 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.