相关论文: Swarming models with specular boundary condition a…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
We study the mean-field limit of the Atlas model and its connection to SDEs with dependence on the distribution of hitting and local times. The Atlas model describes a system of Brownian particles on the real line, where only the lowest…
Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of…
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…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity…
We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition…
We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified…
We propose a stationary system that might be regarded as a migration model of some population abandoning their original place of abode and becoming part of another population, once they reach the interface boundary. To do so, we show a…
The influence that intrinsic local density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the…
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on…
We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e. each Brownian particle can convert internal energy to mechanical energy of motion. We assume the…
This work is devoted to the effective macroscopic dynamics of a weakly damped stochastic nonlinear wave equation with a random dynamical boundary condition. The white noises are taken into account not only in the model equation defined on a…
The mean-field stochastic partial differential equation (SPDE) corresponding to a mean-field super-Brownian motion (sBm) is obtained and studied. In this mean-field sBm, the branching-particle lifetime is allowed to depend upon the…