Related papers: Interaction between localized vegetation patches a…
Games with environmental feedback have become a crucial area of study across various scientific domains, modelling the dynamic interplay between human decisions and environmental changes, and highlighting the consequences of our choices on…
We study numerically local models for the mechanical contact between two solids with rough surfaces. When the solids softly touch either through adhesion or by a small normal load $L$, contact only forms at isolated patches and fluids can…
A simple model is suggested by assuming an effective interaction at the crossing point of the two curves, the Schwarzschild radius and the Compton wave length, that is at the Planck length and Planck mass. It is argued that there would be a…
We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics…
We consider a system of $n$ nonlocal interaction evolution equations on $\mathbb{R}^d$ with a differentiable matrix-valued interaction potential $W$. Under suitable conditions on convexity, symmetry and growth of $W$, we prove…
The present paper is devoted to the study of a simple model of interacting electrons in a random background. In a large interval $\Lambda$, we consider $n$ one dimensional particles whose evolution is driven by the Luttinger-Sy model, i.e.,…
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…
The coexistence of multiple phytoplankton species despite their reliance on similar resources is often explained with mean-field models assuming mixed populations. In reality, observations of phytoplankton indicate spatial aggregation at…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
We report on a computer simulation and integral equation study of a simple model of patchy spheres, each of whose surfaces is decorated with two opposite attractive caps, as a function of the fraction $\chi$ of covered attractive surface.…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…
In the present work we extend the Bak-Sneppen model for biological evolution by introducing local interactions between species. This ``environmental'' perturbation can modify the intrinsic fitness of each element of the ecology, leading to…
Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme.…
A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in…
Interacting particle systems provide a fundamental framework for modeling collective behavior in biological, social, and physical systems. In many applications, stochastic perturbations are essential for capturing environmental variability…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Vegetation patterns are a characteristic feature of semi-arid regions. On hillsides these patterns occur as stripes running parallel to the contours. The Klausmeier model, a coupled reaction-advection-diffusion system, is a deliberately…