Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

TL;DR

This paper investigates intermingled basins of attraction in ecological dynamical systems, using periodic-orbit theory and scaling laws to understand their structure and implications for predictability in species extinction scenarios.

Contribution

It introduces a quantitative analysis of intermingled basins in ecological models through periodic-orbit theory and scaling laws, linking theoretical predictions with exact results.

Findings

Scaling laws agree with stochastic model predictions

Exact scaling exponent derived for specific models

Intermingled basins impact ecological predictability

Abstract

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.