Automatic simplification of systems of reaction–diffusion equations by a posteriori analysis

Abstract

Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44–52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction–diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique.