相关论文: Swarming models with specular boundary condition a…
The influence of crowding on the diffusion of tagged particles in a dense medium is investigated in the framework of a mean-field model, derived in the continuum limit from a microscopic stochastic process with exclusion. The probability…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…
We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…
We propose and analyze a framework for discrete-time robust mean-field control problems under common noise uncertainty. In this framework, the mean-field interaction describes the collective behavior of infinitely many cooperative agents'…
We study environmental echoes induced by a weak potential barrier outside a Schwarzschild black hole. In the low-finesse limit, the time domain response is governed by a sequence of transient wave packets formed by finite round-trip…
We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system we use a collision model…
Interacting particle or agent systems that display a rich variety of swarming behaviours are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and…
In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
The noise of signals or currents consisting from a sequence of pulses, elementary events or moving discrete objects (particles) is analyzed. A simple analytically solvable model is investigated in detail both analytically and numerically.…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
In this paper we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together…
We study the role of multiplicative colored noise for different values of the correlation time $\tau_c$ in the dynamics of two competing species, described by generalized Lotka-Volterra equations. The multiplicative colored noise models the…
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…
We present a numerical method that allows a formation of communicating agents to target the boundary of a time dependent concentration by following a time dependent concentration gradient. The algorithm motivated by \cite{MB, BKM}, allows…
We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's…
An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added…