Bifurcation and hydra effect of a plant-herbivore model with herbivore harvesting

Abstract

Adaptive management of herbivore populations during grassland plant degradation serves as a critical strategy for sustaining ecosystem stability. To address this imperative, establishing a mechanistic grassland resourceherbivore model that incorporates herbivore harvesting and rigorously evaluating harvesting’s impact on system stability holds significant ecological and practical relevance. This study develops a continuous-time plant-herbivore model with an explicit herbivore harvesting term. We first conduct a comprehensive dynamical analysis, characterizing the existence and local stability of the system’s boundary equilibria and interior equilibrium point. This analysis yields precise threshold conditions governing ecosystem stability versus collapse. Subsequently, by designating the herbivore harvesting rate as the primary bifurcation parameter, we demonstrate that the model exhibits rich nonlinear dynamics, including bistability (coexistence of alternative stable states), Hopf bifurcation and the hydra effect (paradoxical increase in herbivore abundance with increased harvesting mortality). Numerical simulations further validated the theoretical analysis.