# Rise and Fall of Periodic Patterns for a Generalized Klausmeier–Gray–Scott Model

@article{Stelt2013RiseAF, title={Rise and Fall of Periodic Patterns for a Generalized Klausmeier–Gray–Scott Model}, author={Sjors van der Stelt and Arjen Doelman and Geertje Hek and Jens D. M. Rademacher}, journal={Journal of Nonlinear Science}, year={2013}, volume={23}, pages={39-95} }

In this paper we introduce a conceptual model for vegetation patterns that generalizes the Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284:1826–1828, 1999). Our model not only incorporates downhill flow, but also linear or nonlinear diffusion for the water component.To relate the model to observations and simulations in ecology, we first consider the onset of pattern formation through a Turing or a Turing–Hopf bifurcation. We perform a Ginzburg–Landau…

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