Bifurcation analysis of a plant-herbivore model with toxin-determined functional response

A system of ordinary differential equations is considered which models the plant-herbivore interactions mediated by a toxin-determined functional response. The new functional response is a modification of the traditional Holling Type 11 functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically. (C) 2008 Elsevier Inc. All rights reserved.