Related papers: Assessing the robustness of spatial pattern sequen…
A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps -> labyrinth -> spots", that occurs as a parameter representing precipitation…
The dryland vegetation model proposed by Rietkerk and collaborators has been explored from a bifurcation perspective in several previous studies. Our aim here is to explore in some detail the bifurcation phenomena present when the…
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…
This paper delves into a systematically reduced plant system proposed by Ja\"ibi et al. [Phys. D, 2020] in arid area. They used the method of geometric singular perturbation to study the existence of abundant orbits. Instead, we deliberate…
Several theoretical models predict that spatial patterning increases ecosystem resilience. However, these predictions rely on simplifying assumptions, such as assuming isotropic and infinitely large ecosystems, and empirical evidence…
We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations.…
From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple…
We develop a model for investigating the impact of rainstorm variability on the formation of banded vegetation patterns in dryland ecosystems. Water input, during rare rainstorms, is modeled as an instantaneous kick to the soil water. The…
Dryland vegetation ecosystems are known to be susceptible to critical transitions between alternative stable states when subjected to external forcing. Such transitions are often discussed through the framework of bifurcation theory, but…
Due to climatic changes, excessive grazing, and deforestation, semi-arid and arid ecosystems are vulnerable to desertification and land degradation. As aridity increases, vegetation cover often self-organizes into spatial patterns before…
The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including…
We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…
Self-organized spatial patterns of vegetation are frequent in drylands and, because pattern shape correlates with water availability, they have been suggested as important indicators of ecosystem health. However, the mechanisms underlying…
Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result…
Dryland vegetation can survive water stress by forming spatial patterns but is often subjected to herbivory as an additional stress that puts it at risk of desertification. Understanding the mutual relationships between vegetation…
Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…
The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…
In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high…