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Patterned vegetation, tipping points, and the rate of climate change

Published online by Cambridge University Press:  23 June 2015

YUXIN CHEN ,
THEODORE KOLOKOLNIKOV ,
JUSTIN TZOU  and
CHUNYI GAI
YUXIN CHEN
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, USA
THEODORE KOLOKOLNIKOV
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada email: tkolokol@gmail.com
JUSTIN TZOU
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada email: tkolokol@gmail.com
CHUNYI GAI
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada email: tkolokol@gmail.com
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Abstract

When faced with slowly depleting resources (such as decrease in precipitation due to climate change), complex ecological systems are prone to sudden irreversible changes (such as desertification) as the resource level dips below a tipping point of the system. A possible coping mechanism is the formation of spatial patterns, which allows for concentration of sparse resources and the survival of the species within “ecological niches” even below the tipping point of the homogeneous vegetation state. However, if the change in resource availability is too sudden, the system may not have time to transition to the patterned state and will pass through the tipping point instead, leading to extinction. We argue that the deciding factors are the speed of resource depletion and the amount of the background noise (seasonal climate changes) in the system. We illustrate this phenomenon on a model of patterned vegetation. Our analysis underscores the importance of, and the interplay between, the speed of climate change, heterogeneity of the environment, and the amount of seasonal variability.

Keywords

delayed bifurcationsstochastic PDE'sTuring instabilityclimate changepatched vegetation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 6 , December 2015 , pp. 945 - 958
Copyright
Copyright © Cambridge University Press 2015 

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