Transitions between patterned states in vegetation models for semiarid ecosystems

Karna Gowda, Hermann Riecke, Mary Silber

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

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.

Original languageEnglish (US)
Article number022701
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume89
Issue number2
DOIs
StatePublished - Feb 3 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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