Abstract
Vegetation and plateau pika are two key species in alpine meadow ecosystems on the Tibetan Plateau. It is frequently observed on the field that plateau pika reduces the carrying capacity of vegetation and the mortality of plateau pika increases along with the increasing height of vegetation. This motivates us to propose and study a predator-prey model with state-dependent carrying capacity. Theoretical analysis and numerical simulations show that the model exhibits complex dynamics including the occurrence of saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation, and the coexistence of two stable equilibria.
Highlights
The alpine meadow is an important ecosystem in China that provides important ecological services such as purification of air and water, maintenance of biodiversity, decomposition of wastes, soil and vegetation generation and renewal, etc
In a healthy alpine meadow ecosystem, the amount of vegetation and the plateau pika population density should maintain at a constant level, that is, the vegetation and the plateau pika populations should be near an equilibrium rather than a limit cycle
We have proposed a predator-prey model to understand the interplay between vegetation and plateau pika in an alpine meadow ecosystem
Summary
The alpine meadow is an important ecosystem in China that provides important ecological services such as purification of air and water, maintenance of biodiversity, decomposition of wastes, soil and vegetation generation and renewal, etc. Predator-prey model, bifurcation, alpine meadow, plateau pika. Hopf bifurcation at p pH r2 + αμ + Γ resulting in the appearance of a stable limit cycle for p > pH. To illustrate our main results and the above bifurcation scenarios, we numerically sketch two representative bifurcation diagrams To this end, we take parameter values comparable to values in the literature. In the alpine meadow ecosystem, both vegetation and plateau pika serve important ecological functions and they are supposed to coexist. In the case that E2 is unstable, a limit cycle exists and both populations of vegetation and plateau pika undergo sustained oscillations. In a healthy alpine meadow ecosystem, the amount of vegetation and the plateau pika population density should maintain at a constant level, that is, the vegetation and the plateau pika populations should be near an equilibrium rather than a limit cycle.
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