2017/09/19 by C. B. Ward, P. G. Kevrekidis, Ward, C. B. +3
Environmental Science · #Animal Ecology and Behavior Studies #Ecology and Vegetation Dynamics Studies #Ecosystem dynamics and resilience #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1709.06527
openalex publication_date 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dryland vegetation model proposed by Rietkerk and collaborators has been explored from a bifurcation perspective in several previous studies. Our aim here is to explore in some detail the bifurcation phenomena present when the coefficients of the model are allowed to vary in a wide range of parameters. In addition to the primary bifurcation parameter, the precipitation, we allow the two infiltration rate parameters to vary as well. We find that these two parameters control the size and stability of nonhomogeneous biomass states in a way that can be predicted. Further, they control when certain homogeneous and inhomogeneous (in space) periodic (in time) orbits exist. Finally, we show that the model possesses infinitely many unphysical steady state branches. We then present a modification of the model which eliminates these unphysical solutions, and briefly explore this new model for a fixed set of parameters.