Bifurcation Analysis of a Model for Plant-Herbivore Interactions

Dr. Zhilan Feng

Department of Mathematics
Purdue University

1 April 2011
218 Shelby Center
3:00 (Refreshements at 2:30)

Abstract

Earlier models of plant-herbivore interactions relied on forms of functional response that related rates of ingestion by herbivores to mechanical or physical attributes such as bite size and rate. These models fail to predict a growing number of findings that implicate chemical toxins as important determinants of plant-herbivore dynamics. Specifically, considerable evidence suggests that toxins set upper limits on food intake for many species of herbivorous vertebrates. Herbivores feeding on toxin-containing plants must avoid saturating their detoxification systems, which often occurs before ingestion rates are limited by mechanical handling of food items. We developed mathematical models with toxin-determined functional responses to study the effects of inter-specific plant competition, herbivory, and a plant's toxic defenses against herbivores on vegetation dynamics. The new models exhibit much more complex dynamics including Hopf and homoclinic bifurcations.