Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments.
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Summary
A detailed study of the patterned solutions in the full nonlinear model is presented, using numerical bifurcation analysis of both the pattern odes and the model pdes to show that patterns exist for a wide range of rainfall levels, and in particular for much lower rainfall than have been considered by previous authors.
- Type
- article
- Published
- 2007-02-01
- Cited by
- 122
- References
- 32
- OpenAlex
- https://openalex.org/W1977031359
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:12309074
Keywords
Nonlinear system, Arid, Vegetation (pathology), Bifurcation, Pattern formation
References
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- Banded Vegetation Patterning in Arid and Semiarid Environments
- Some vegetation patterns in the Republic of the Sudan
- VODE: a variable-coefficient ODE solver
- An Analysis of Vegetation Stripe Formation in Semi-Arid Landscapes
- Simulating the dynamics of a vegetation mosaic: a spatialized functional model
- A model simulating the genesis of banded vegetation patterns in Niger
- THE BUTANA GRASS PATTERNS
- Some Practical Experience with the Time Integration of Dissipative Equations
- Regular and irregular patterns in semiarid vegetation
- Vegetation spots and stripes: Dissipative structures in arid landscapes
- The colonization of bare areas in two-phase mosaics of an arid ecosystem
- The response of two woody species to the conditions created by a shifting ecotone in an arid ecosystem.
- On the origin of tiger bush
- Vegetation patterns in the semi-desert plains of British Somaliland.
- Periodic spotted patterns in semi‐arid vegetation explained by a propagation‐inhibition model
- A model for the explanation of vegetation stripes (tiger bush)
- Self-Organized Patchiness and Catastrophic Shifts in Ecosystems
- Self‐Organization of Vegetation in Arid Ecosystems
- VEGETATION PATTERN FORMATION IN SEMI-ARID GRAZING SYSTEMS
Cited by
- When does colonisation of a semi-arid hillslope generate vegetation patterns?
- Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts.
- Applications of nonequilibrium statistical physics to ecological systems
- Applications of stability theory to ecological problems
- Rhombic Analysis Extension of a Plant-Surface Water Interaction-Diffusion Model for Hexagonal Pattern Formation in an Arid Flat Environment
- Localised pattern formation in a model for dryland vegetation
- Pattern dynamics in a vegetation model with time delay
- Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system
- Velocities, celerities and the basin of attraction in catchment response
- Vegetation pattern formation in a fog-dependent ecosystem.
- Using wavelength and slope to infer the historical origin of semiarid vegetation bands
- Beyond Turing: The response of patterned ecosystems to environmental change
- A minimal model of soil water–vegetation interactions forced by stochastic rainfall in water-limited ecosystems
- Determinants and dynamics of banded vegetation pattern migration in arid climates
- Patterned vegetation and rainfall intermittency.
- Instability of periodic traveling wave solutions in a modified FitzHugh-Nagumo model for excitable media
- Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations
- A new statistical dynamic analysis on vegetation patterns in land ecosystems
- Influence of time delay and nonlinear diffusion on herbivore outbreak
- Environmental modulation of self‐organized periodic vegetation patterns in Sudan
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