相关论文: Stochastic and Coarse-Grained Two-Dimensional Mode…
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 introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
In this paper we consider an interacting particle system in $\mathbb{R}^d$ modelled as a system of $N$ stochastic differential equations driven by L\'evy processes. The limiting behaviour as the size $N$ grows to infinity is achieved as a…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…
We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
The mean-field dynamics of a collection of stochastic agents with local versus nonlocal interactions is studied via analytically soluble models. The nonlocal interactions result from a barycentric modulation of the observation range of the…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…