2019/11/26 by Bartosz J. Bartmanski, Ruth E. Baker, Bartmanski, Bartosz J. +1
Computer Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1911.11645
openalex publication_date 2019/11/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
By discretising space into compartments and letting system dynamics be\ngoverned by the reaction-diffusion master equation, it is possible to derive\nand simulate a stochastic model of reaction and diffusion on an arbitrary\ndomain. However, there are many implementation choices involved in this\nprocess, such as the choice of discretisation and method of derivation of the\ndiffusive jump rates, and it is not clear a priori how these affect model\npredictions. To shed light on this issue, in this work we explore how a variety\nof discretisations and method for derivation of the diffusive jump rates affect\nthe outputs of stochastic simulations of reaction-diffusion models, in\nparticular using Turing's model of pattern formation as a key example. We\nconsider both static and uniformly growing domains and demonstrate that, while\nonly minor differences are observed for simple reaction-diffusion systems,\nthere can be vast differences in model predictions for systems that include\ncomplicated reaction kinetics, such as Turing's model of pattern formation. Our\nwork highlights that care must be taken in using the reaction-diffusion master\nequation to make predictions as to the dynamics of stochastic\nreaction-diffusion systems.\n