Contribution in an anthology

Appeared in: Modelling Complex Ecological Dynamics : an introduction into ecological modelling for students, teachers & scientists

Editor list: Jopp, F; Reuter, H; Breckling, B

Publication year: 2011

Pages: 67-91

ISBN: 978-3-642-05028-2

eISBN: 978-3-642-05029-9

DOI Link: https://doi.org/10.1007/978-3-642-05029-9_6

Abstract: 

Differential equations represent a centrally important ecological
modelling approach. Originally developed to describe quantitative
changes of one or more variables in physics, the approach was imported
to model ecological processes, in particular population dynamic
phenomena. The chapter describes the conceptual background of ordinary
differential equations and introduces the different types of dynamic
phenomena which can be modelled using ordinary differential equations.
These are in particular different forms of increase and decline, stable
and unstable equilibria, limit cycles and chaos. Example equations are
given and explained. The Lotka–Volterra model for predator–prey
interaction is introduced along with basic concepts (e.g. direction
field, zero growth isoclines, trajectory and phase space) which help to
understand dynamic processes. Knowing basic characteristics, it is
possible for a modeller to construct equation systems with specific
properties. This is exemplified for multiple stability and hysteresis (a
sudden shift of the models state when certain stability conditions come
to a limit). Only very few non-linear ecological models can be solved
analytically. Most of the relevant models require numeric approximation
using a simulation tool.

Harvard Citation style: Breckling, B., Jopp, F. and Reuter, H. (2011) Ordinary Differential Equations, in Jopp, F., Reuter, H. and Breckling, B. (eds.) Modelling Complex Ecological Dynamics : an introduction into ecological modelling for students, teachers & scientists. Berlin: Springer, pp. 67-91. https://doi.org/10.1007/978-3-642-05029-9_6

APA Citation style: Breckling, B., Jopp, F., & Reuter, H. (2011). Ordinary Differential Equations. In Jopp, F., Reuter, H., & Breckling, B. (Eds.), Modelling Complex Ecological Dynamics : an introduction into ecological modelling for students, teachers & scientists (pp. 67-91). Springer. https://doi.org/10.1007/978-3-642-05029-9_6