Bifurcations and Dynamic Complexity in Simple Ecological Models

Abstract

Nature is complex. Despite this acknowledged fact, there is a rationale for constructing oversimplified mathematical caricatures of reality: one hopes to capture the essence of observed patterns and processes without becoming enmeshed in the details. This strategy has enjoyed considerable success in physics and chemistry, and there is a growing literature exploring simple mathematical models in ecology and debating their usefulness. It is not our aim to contribute to this debate, as such. Rather we wish to point out a disconcerting property of many very simple, deterministic models which allows them to behave in extremely complicated ways.