title: Transitions between patterned states in vegetation models for semiarid ecosystems.
abstract: A feature common to many models of vegetation pattern formation in semiarid ecosystems is a sequence of qualitatively different patterned states, "gaps → labyrinth → spots," that occurs as a parameter representing precipitation decreases. We explore the robustness of this "standard" sequence in the generic setting of a bifurcation problem on a hexagonal lattice, as well as in a particular reaction-diffusion model for vegetation pattern formation. Specifically, we consider a degeneracy of the bifurcation equations that creates a small bubble in parameter space in which stable small-amplitude patterned states may exist near two Turing bifurcations. Pattern transitions between these bifurcation points can then be analyzed in a weakly nonlinear framework. We find that a number of transition scenarios besides the standard sequence are generically possible, which calls into question the reliability of any particular pattern or sequence as a precursor to vegetation collapse. Additionally, we find that clues to the robustness of the standard sequence lie in the nonlinear details of a particular model.
authors.affiliation: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Karna
authors.initials: K
authors.lastname: Gowda
authors.affiliation: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Hermann
authors.initials: H
authors.lastname: Riecke
authors.affiliation: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Mary
authors.initials: M
authors.lastname: Silber
mesh_terms: D003198:Computer Simulation; D003889:Desert Climate; D017753:Ecosystem; D008954:Models, Biological; D010363:Pattern Recognition, Automated / Q000379:methods*; D063245:Plant Development / Q000502:physiology*; D010944:Plants / Q000033:anatomy & histology*