Related papers: Beyond water limitation in vegetation-autotoxicity…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
Patterns of vegetation are a characteristic feature of many semi-arid regions. The limiting resource in these ecosystems is water, which is added to the system through short and intense rainfall events that cause a pulse of biological…
Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…
We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending upon boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an…
Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
A packed community of exponentially proliferating microbes will spread in size exponentially. However, due to nutrient depletion, mechanical constraints, or other limitations, exponential proliferation is not indefinite, and the spreading…
In the context of multistability driven diseases, like cancer, spatiotemporal plasticity plays a significant role to achieve a spectrum of phenotypic variations. The interplay between gene regulatory networks and environmental factors, such…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
The savanna biome is characterised by a continuous vegetation cover, comprised of herbaceous and woody plants. The coexistence of species in arid savannas, where water availability is the main limiting resource for plant growth, provides an…
In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. We consider a two-component…
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
In this work, we present and analyze a general framework for vegetation dynamics in arid and semi-arid ecosystems in which non-local interactions are purely competitive. The generality of the formulation enables a systematic search for…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple…