A three variable differential equation model for gypsy moth population dynamics

Abstract

The dynamics of gypsy moth, Lymantria dispar (Lepidoptera: Lymantriidae), populations are extremely complex. As a result, many of the models which have been proposed to model these populations are likewise very complicated. This complexity makes analysis of the underlying dynamics difficult. In this work a model is proposed which involves only three variables: gypsy moth biomass density, foliage biomass density and natural enemy biomass density. The dynamics of this model are shown to include period doubling as a route to chaos, among other interesting nonlinear phenomena. The model also evidences similar behavior to that noted from field studies in which researchers attempted to artificially stimulate outbreaks of gypsy moths. While these attempts failed in nature and in the model, the model predicts that under certain circumstances it may be possible to stimulate these outbreaks.