Related papers: Minimal stochastic field equations for one-dimensi…

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…

In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…

Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by…

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

Collective motion - or flocking - is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean…

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from…

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real…

Two hallmarks of non-equilibrium systems, from active colloids to animal herds, are agents motility and nonreciprocal interactions. Their interplay creates feedback loops leading to complex spatiotemporal dynamics crucial to understand and…

We present a novel microscopic stock market model consisting of a large number of random agents modeling traders in a market. Each agent is characterized by a set of parameters that serve to make iterated predictions of two successive…

We consider a model of Non-Brownian self-propelled particles with anti-alignment interactions where particles try to avoid each other by attempting to turn into opposite directions. The particles undergo apparent Brownian motion, even…

Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…

We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent…

The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are…

We study inherently chiral self-propelled particles, self-rotating at a fixed frequency, in two dimensions, subjected to nematic alignment interactions and rotational noise. By means of both, homogeneous and spatially resolved mean field…

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…

In this work, we consider a multi-population system where the dynamics of each agent evolve according to a system of stochastic differential equations in a general functional setup, determined by the global state of the system. Each agent…

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…

We introduce a mesocopic modeling approach for active systems. The continuum model allows to consider microscopic details as well as emerging macroscopic behavior and can be considered as a minimal continuum model to describe generic…

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…

Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely…