We consider a generic interaction-redistribution model of vegetation dynamics to investigate the formation of patchy vegetation in semi-arid and arid landscapes. First, we perform a weakly nonlinear analysis in the neighborhood of the symmetry-breaking instability. Following this analysis, we construct the bifurcation diagram of the biomass density. The weakly nonlinear analysis allows us to establish the condition under which the transition from super- to subcritical symmetry-breaking instability takes place. Second, we generate a random distribution of localized patches of vegetation numerically. This behavior occurs in regimes where a bare state coexists with a uniform biomass density. Field observations allow to estimate the total biomass density and the range of facilitative and competitive interactions.
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September 2020
Research Article|
September 21 2020
Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model
Special Collection:
Instabilities and Nonequilibrium Structures
M. Messaoudi;
M. Messaoudi
1
Faculté des Sciences, Université Libre de Bruxelles (U.L.B)
, CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
2
Faculté des Sciences, Université Moulay Ismail, Dynamique des Systémes Complexes et Simulation Numérique
, B.P. 11201, Zitoune, Meknès, Morocco
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M. G. Clerc
;
M. G. Clerc
3
Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
, Casilla 487-3, Santiago, Chile
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E. Berríos-Caro
;
E. Berríos-Caro
3
Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
, Casilla 487-3, Santiago, Chile
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D. Pinto-Ramos;
D. Pinto-Ramos
3
Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
, Casilla 487-3, Santiago, Chile
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M. Khaffou
;
M. Khaffou
2
Faculté des Sciences, Université Moulay Ismail, Dynamique des Systémes Complexes et Simulation Numérique
, B.P. 11201, Zitoune, Meknès, Morocco
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A. Makhoute
;
A. Makhoute
a)
1
Faculté des Sciences, Université Libre de Bruxelles (U.L.B)
, CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
2
Faculté des Sciences, Université Moulay Ismail, Dynamique des Systémes Complexes et Simulation Numérique
, B.P. 11201, Zitoune, Meknès, Morocco
a)Author to whom correspondence should be addressed: abdelkader.makhoute@ulb.ac.be
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M. Tlidi
M. Tlidi
1
Faculté des Sciences, Université Libre de Bruxelles (U.L.B)
, CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
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a)Author to whom correspondence should be addressed: abdelkader.makhoute@ulb.ac.be
Note: This article is part of the Focus Issue, instabilities and Nonequilibrium Structures.
Chaos 30, 093136 (2020)
Article history
Received:
May 26 2020
Accepted:
August 24 2020
Citation
M. Messaoudi, M. G. Clerc, E. Berríos-Caro, D. Pinto-Ramos, M. Khaffou, A. Makhoute, M. Tlidi; Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model. Chaos 1 September 2020; 30 (9): 093136. https://doi.org/10.1063/5.0011010
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