Cascading thresholds to heteroclinicity in an ecosystem model

Abstract

Using a model of three consumer/resource pairs coupled in an ecosystem model, previous work has demonstrated a particular dynamical behavior in which a switch from a chaotic attractor to a heteroclinic cycle is the underlying mechanism that causes extinction of some components of the system. The complex bifurcation sequence from chaos to heteroclinic cycle in this model is described using numerical methods. Evidence is presented suggesting a structure of nested manifolds that gradually reverse stabilities as the bifurcation parameter changes.