Dynamics of a plant-herbivore model subject to allee effects with logistic growth of plant biomass

Abstract

This paper examines the relationship between herbivores and plants with a strong Allee effect. When the plant reaches a particular size, the herbivore attacks it. We use the logistic equation to model plant growth and analyze its behavior without herbivores before investigating their interactions. Our study investigates the equilibrium points and their stability, discovering that different fixed points can become unstable due to various bifurcations such as transcritical, saddle-node, period-doubling, and Neimark-Sacker bifurcations. We have identified the Allee threshold, which, if exceeded, can cause both populations to become extinct below that level. However, we have discovered a coexistence equilibrium that is locally asymptotically stable for a range of parameter values above that threshold. Our additional numerical simulations suggest that this area of stability can be expanded. Our results indicate that this system is highly responsive to its parameters. We compare our findings to those of a system without strong Allee effects and conduct numerical simulations to verify our results. By including the Allee effect in the plant population, we enrich the local and global dynamics of the system.