Modeling of one-dimensional spatial effects on the spread of gypsy moths

Modeling of gypsy moth (Lymantria dispar (Lepidoptera: Lymantriidae)) populations is extremely complex. In this work, a recently proposed model for spatially homogeneous populations which involves only three variables has been modified to study the spread of gypsy moth populations. The dynamics of this model includes waves of modulating amplitude which propagate in the spatio-temporal domain. Under certain conditions these spatial inhomogeneities eventually decay, resulting in spatially homogeneous behavior. Under other conditions they continue to exist, and in one case it was observed that appropriate perturbations on a chaotic system led to the establishment of a constant-shape, constant-velocity traveling wave. In this work we also study the effects of attempting to stimulate outbreaks by the implantation of a large number of gypsy moth egg masses at a specific location, as well as the effects of repeated transportation of egg masses to a single site (such as a camp ground). In addition, we report the results of simulating the application of pesticides.