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Mathematics 2017, 5(4), 69; https://doi.org/10.3390/math5040069

Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation

Institute of Environmental Systems Research, School of Mathematics, Computer Science, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany
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Received: 5 October 2017 / Revised: 3 November 2017 / Accepted: 14 November 2017 / Published: 23 November 2017
(This article belongs to the Special Issue Progress in Mathematical Ecology)
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Abstract

Semi-arid ecosystems made up of patterned vegetation, for instance, are thought to be highly sensitive. This highlights the importance of understanding the dynamics of the formation of vegetation patterns. The most renowned mathematical model describing such pattern formation consists of two partial differential equations and is often referred to as the Klausmeier model. This paper provides analytical and numerical investigations regarding the influence of different parameters, including the so-far not contemplated evaporation, on the long-term model results. Another focus is set on the influence of different initial conditions and on environmental noise, which has been added to the model. It is shown that patterning is beneficial for semi-arid ecosystems, that is, vegetation is present for a broader parameter range. Both parameter variability and environmental noise have only minor impacts on the model results. Increasing mortality has a high, nonlinear impact underlining the importance of further studies in order to gain a sufficient understanding allowing for suitable management strategies of this natural phenomenon. View Full-Text
Keywords: Klausmeier model; pattern formation; self-organization; reaction–diffusion–advection model; environmental noise Klausmeier model; pattern formation; self-organization; reaction–diffusion–advection model; environmental noise
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Köhnke, M.C.; Malchow, H. Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation. Mathematics 2017, 5, 69.

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