The effect of resource quality on the dynamics of a resource-consumer model

In this paper, inspired by the forage-maturation hypothesis, we propose and investigate a novel resource-consumer model that incorporates forage quality, represented by digestibility, which declines exponentially with increasing biomass. Our aim is to reveal the coupled effects of resource biomass and quality on system dynamics. To this end, we first analyze the existence and stability of equilibria as well as the possible bifurcations the model undergoes, and then perform some numerical simulations to illustrate and complement the obtained theoretical results. Compared to the traditional resource-consumer model with no consideration of resource quality, our model can exhibit much more complex dynamics, including rich bifurcation phenomena such as Hopf, transcritical, saddle-node, homoclinic as well as cusp and Bogdanov-Takens bifurcations, and two types of bistability. Both theoretical and numerical findings indicate that large resource biomass with low quality can lead to the extinction of consumers; however, for a herbivore population with low mortality rate, a moderate level of forage quality is more conducive to its persistence. These can provide fresh insights into maintaining the ecological balance within forage-herbivore systems.