## 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 language | English (US) |
---|---|

Article number | 022701 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 89 |

Issue number | 2 |

DOIs | |

State | Published - Feb 3 2014 |

## ASJC Scopus subject areas

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