Related papers: A Stochastic Analysis of Particle Systems with Pai…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
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…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
Stochastic boundary conditions for interactions with a particle reservoir are discussed in many-particle systems. We introduce the boundary conditions with the injection rate and the momentum distribution of particles coming from a particle…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
In this paper, we consider a multi-agent system consisting of mobile agents with second-order dynamics. The communication network is determined by the so-called topological interaction rule: agents interact with a fixed number of their…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…
An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of…
We consider a basic stochastic particle system consisting of $N$ identical particles with isotropic $k$-particle synchronization, $k\geq 2$. In the limit when both number of particles $N$ and time $t=t(N)$ grow to infinity we study an…
We investigate in detail a recent model of colliding mobile agents [Phys. Rev. Lett.~96, 088702], used as an alternative approach to construct evolving networks of interactions formed by the collisions governed by suitable dynamical rules.…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
In this work the system of agents is applied to establish a model of the nonlinear distributed signal processing. The evolution of the system of the agents - by the prediction time scale diversified trend followers, has been studied for the…
We study a class of graphon particle systems with time-varying random coefficients. In a graphon particle system, the interactions among particles are characterized by the coupled mean field terms through an underlying graphon and the…