Maybank Philip J, Whiteley Jonathan P
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom.
Math Biosci. 2014 Feb;248:146-57. doi: 10.1016/j.mbs.2013.12.011. Epub 2014 Jan 11.
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.
生物学和生理学中的许多数学模型都由非线性微分方程组表示。近年来，为了解释现有的大量数据，这些模型变得越来越复杂。建模者的一个关键作用是确定模型的哪些组件对给定的观测行为影响最大。最近，基于后验分析，一种自动履行这一作用的方法已被开发用于非线性初值常微分方程[J.P.怀特利，使用后验分析的模型约简，数学生物科学225(2010)44-52]。在本文中，我们将这种模型约简技术扩展到稳态和与时间相关的非线性反应扩散系统的应用中。从生物学中提取的示例问题用于证明该技术的适用性。
