Oscillatory phenomena of nutrient-plant-herbivore system with time lag: a mathematical approach

Abstract

In the present study we consider a nutrient-based model of nutrient-plant-herbivore interaction with a delayed nutrient recycling and incorporate the number of herbivores attacking the plants follows Holling type III functional response. We have derived the conditions for asymptotic stability of the steady state and also estimated the length of the delay preserving the stability. The criterion for existence of Hopf-type small amplitude periodic oscillations of plant biomass and herbivore numbers are derived. Finally, all the analytical results are interpreted ecologically and compared with the computer simulation.