Analysis of differential equation models in biology: A case study for clover meristem populations

Abstract

Biological scenarios are given in which it is more appropriate to use differential equations, rather than the more commonly used difference equations, to model the processes occurring. The relative merits of small simple models and large‐scale simulation models are compared. A simple differential equation model (dynamical system) for clover, based on meristem numbers, is outlined and analysed mathematically. The model possesses two steady states, and a threshold condition dictating which of these steady states is ultimately achieved is presented. The advantages in nondimensional‐ising the model are demonstrated, highlighted by reduction of parameter dependence and increased efficiency over conventional means of sensitivity analysis.

Keywords:

• stability analysis
• sensitivity analysis
• steady states
• growing points
• buds
• meristems