Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 6 - Stochastic Reaction–Diffusion Models

  • 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 160-191

  • Summary

    This chapter discusses stochastic approaches for modelling chemical reactions (introduced in Chapter 1) and molecular diffusion at the same time. The presented stochastic reaction–diffusion processes add chemical reactions to the two position-jump models of molecular diffusion that are introduced in Chapter 4: the compartment-based approach (described by the reaction–diffusion master equation) and the SDE-based approach, which gives the Brownian dynamics. Basic principles of each approach are explained using an example that includes only zeroth- and first-order chemical reactions. This is followed by discussion of more complicated systems when some chemical species are subject to higher-order chemical reactions. The reaction radius, reaction probability and the choice of the compartment size are studied in detail. The chapter concludes with the discussion of applications to pattern formation in biology, including stochastic French flag model and stochastic Turing patterns.