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

Merlin C. Köhnke and Horst Malchow
Additional contact information
Merlin C. Köhnke: Institute of Environmental Systems Research, School of Mathematics, Computer Science, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany
Horst Malchow: Institute of Environmental Systems Research, School of Mathematics, Computer Science, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany

Mathematics, 2017, vol. 5, issue 4, 1-19

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.

Keywords: Klausmeier model; pattern formation; self-organization; reaction–diffusion–advection model; environmental noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/5/4/69/pdf (application/pdf)
https://www.mdpi.com/2227-7390/5/4/69/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:5:y:2017:i:4:p:69-:d:120120

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().