Order and Chaos in Ecological Systems

Abstract

Systems of differential equations exhibiting complex periodic or chaotic behavior can sometimes be associated with one—dimensional mappings (difference equations) which encapsulate the properties of the attractor governing the full n—dimensional system. Recent advances make it possible to reconstruct the underlying attractor, and hence the one—dimensional map, from time—series data for a single state variable (species). The present paper illustrates this technique with reference to a hypothetical system consisting of a single predator species and two species of victims. Trapping records for Canadian lynx suggest that the method may have application to real—world populations.