Numerical simulation of dynamic systems with R: an introduction

Dynamical systems are found everywhere, in mathematics, physics, chemistry, engineering and business - ecology and aquatic sciences are no exception.

One common approach to describe such systems is by means of differential equations. Following the ideas of Forrester, differential equations appear quite naturally if we describe changes in a system in terms of growth and decay, which together make up a mass balance. A somewhat bigger challenge is to solve these differential equations - some of us may still remember the challenges of differential calculus in high school courses.

Fortunately, computer algorithms allow to solve even complex differential equation systems numerically. This has opened a world of practical applications to be accessible for anyone that has a basic knowledge in scientific computing, or is willing to acquire this knowledge. R is such a scientific computing language that offers powerful methods to solve differential equations. Moreover, some R-packages are especially designed to also solve spatially variable problems that are often found of importance in aquatic sciences.

The introduction will demonstrate selected examples: growth of organisms, predator-prey interaction, spread of diseases, and transport-reaction problems. The formulation of such models in R can be surprisingly compact and close to the mathematical equations.