Affiliation:
1. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
Abstract
We study the dynamics emergent from a two-dimensional reaction–diffusion process modeled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution of cells in a bioactive porous medium, with the evolution of the local cell density depending on a coupled quasi-static fluid flow problem. We demonstrate differences emergent from the choice of a discrete lattice or a continuum for the spatial domain of such a process. We find long-time oscillations and steady states in cell density in both lattice and continuum models, but that the continuum model only exhibits solutions with vertical symmetry, independent of initial data, whereas the finite lattice admits asymmetric oscillations and steady states arising from symmetry-breaking bifurcations. We conjecture that it is the structure of the finite lattice which allows for more complicated asymmetric dynamics. Our analysis suggests that the origin of both types of oscillations is a nonlocal reaction–diffusion mechanism mediated by quasi-static fluid flow.
Funder
Engineering and Physical Sciences Research Council
Royal Society Leverhulme Trust Senior Research Fellowship
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)
Cited by
1 articles.
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