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DY: Fachverband Dynamik und Statistische Physik
DY 70: Poster: Flows, Patterns, Delay, Reaction Diffusion
DY 70.20: Poster
Donnerstag, 15. März 2018, 15:30–18:00, Poster A
Stability and Coexistence of Vegetation Patterns in a Reduced Model — •Florian Dietl1, Fabian Bergmann1, Lisa Rapp1, Ehud Meron2, and Walter Zimmermann1 — 1Theoretische Physik I, Universität Bayreuth, 95440 Bayreuth — 2Blaustein Institutes for Desert Research, Ben Gurion University
We analyze a reduced normal form of a vegetation model for water-limited ecosystems [1]. The model has both finite amplitude homogeneous and spatially periodic solutions, as well as superpositions of the different solutions. We investigate the elementary bifurcations between these states in terms of four coupled, spatially independent nonlinear equations, which are obtained from the original model by a Galerkin-truncation. Among other phenomena, we find for the four coupled equations a transition between a homogeneous vegetation state and a hexagonally modulated state. This and other transitions are characterized and analyzed. We also show that the solutions and bifurcations obtained from the four coupled equations agree over a wide range of parameters with the solutions of the full vegetation model.
[1] E. Gilad et al., J. Theor. Biol. 244, 680 (2007)