Dynamics of a plant-herbivore model with a chemically-mediated numerical response

A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response. This numerical response accounts for the reduction in the herbivore's growth and reproduction due to chemical defenses from plants. It is shown that the system exhibits very rich dynamics including saddle-node bifurcations, Hopf bifurcations, homoclinic bifurcations and co-dimension 2 bifurcations. Numerical simulations are presented to illustrate the occurrence of multitype bistability, limit cycles, homoclinic orbits and heteroclinic orbits. We also discuss the ecological implications of the resulting dynamics