相关论文: On the evolution of slow dispersal in multi-specie…

Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…

We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a uniform parabolicity condition. As the main…

We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between…

A central issue in ecology today is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to the problem of species abundance…

In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the…

The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…

We study a population of $N$ particles, which evolve according to a diffusion process and interact through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field…

In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the…

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein-Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weighted…

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…

We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…

We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric…

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…

We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which…

Data scarcity drives the need for more sample-efficient large language models. In this work, we use the double descent phenomenon to holistically compare the sample efficiency of discrete diffusion and autoregressive models. We show that…

The goal of this note is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It…

We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…

For a class of competition-diffusion nonlinear systems involving fractional powers of the Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove that uniform boundedness implies H\"older boundedness for…

The long time behavior of the dynamics of a fast-slow system of ordinary differential equations is examined. The system is derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow…