Related papers: Beyond water limitation in vegetation-autotoxicity…
Multiscale spatial structure complicates temporal prediction because small-scale spatial fluctuations influence large-scale evolution, yet resolving all scales is often intractable. Standard diffusion models do not address this problem…
This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on…
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such…
In this work, the influence of inertial effects on the formation and evolution of vegetation patterns on sloped arid terrains is investigated from the onset of instability to far-from-equilibrium. Analyses are carried out in a hyperbolic…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
We study the effect of discreteness on various models for patterning in bacterial colonies. In a bacterial colony with branching pattern, there are discrete entities - bacteria - which are only two orders of magnitude smaller than the…
Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are…
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…
We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform an evolutionary self-preservation…
Fire is an indissoluble component of ecosystems, however quantifying the effects of fire on vegetation is challenging task as fire lies outside the typical experimental design attributes. A recent simulation study showed that under…
Vegetation in semi-arid ecosystems frequently organizes into spatially heterogeneous mosaics that regulate ecosystem functioning, productivity, and resilience. These patterns arise from local biological interactions, including facilitation…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blow-up in the model as…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model…
Given the recent increase in wildfires, developing a better understanding of their dynamics is crucial. For this purpose, the advection-diffusion-reaction model has been widely used to study wildfire dynamics. In this study, we introduce…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…