The Application of Catastrophe Theory to Ecological Systems

Jones, D.D. (1975). The Application of Catastrophe Theory to Ecological Systems. IIASA Research Report. IIASA, Laxenburg, Austria: RR-75-015

Preview

Text RR-75-015.pdf Download (1MB) | Preview

Abstract

Catastrophe theory is a new field in mathematical topology that allows the formulation of comprehensive qualitative systems models which have previously eluded rigorous mathematical formulation. Because the models have a topological foundation, many seemingly dissimilar phenomena can be related to a common underlying topological structure. The properties of that structure can then be studied in a convenient form and the conclusions related back to the original problem. This paper provides an introduction to catastrophe theory and defines the principal conditions required for its application. The basic properties of bimodality, discontinuity (catastrophe), hysteresis, and divergence are defined and illustrated using the simplest structures of the theory.

The application of catastrophe theory to ecology is illustrated with the spruce budworm system of eastern Canada. With a minimum of descriptive information about the budworm system, a qualitative catastrophe theory model is hypothesized. This model is rich in its ability to provide predictions on the global behavior of the system. To further check and refine the assumptions of this qualitative model, an existing detailed simulation model is analyzed from the perspective of catastrophe theory. The simulation indeed exhibits a basic underlying structure in agreement with the previously hypothesized model. In this instance catastrophe theory provides a consistent framework with which to analyze and interpret the results of the simulation. These interpretations are not at variance with the first rough qualitative model based only on a small set of descriptive information.

Actions (login required)

View Item