Related papers: Minimal stochastic field equations for one-dimensi…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…
We investigate the effect of cooperative interactions in an ensemble of microorganisms, modelled as self-propelled disk-like and rod-like particles, in a three-dimensional turbulent flow to show flocking as an emergent phenomenon. Building…
In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…
Flocking is ubiquitous in nature and emerges due to short- or long-range alignment interactions among self-propelled agents. Two unfriendly species that antialign or even interact nonreciprocally show more complex collective phenomena,…
Driven non-equilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional…
A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be…
We present a new stochastic particle system on networks which describes the flocking behavior and pattern formation. More precisely, we consider Cucker-Smale particles with decentralized formation control and multiplicative noises on…
The collective motion of self-driven agents is a phenomenon of great interest in interacting particle systems. In this paper, we develop and analyze a model of agent motion in one dimension with periodic boundaries using a stochastic…
We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate and the temperature…
Many biological systems form colonies at high density. Passive granular systems will be jammed at such densities, yet for the survival of biological systems it is crucial that they are dynamic. We construct a phase diagram for a system of…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
Field control provides a practical route to programmable active matter, yet how weak fields modify non-equilibrium coexistence and interfaces remains unclear. To address this, we study a minimal flocking model of active Potts particles…
Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with…
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…
We study the spatial pattern formation and emerging long range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a…
In this article, we consider the problem of stabilizing stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. Most existing works on modeling and…
Collective behavior in biological systems was first captured by the Vicsek model, in which particles align their velocities in the average direction of neighbors, leading to coherent motion and showing an order-disorder transition. However,…
Coordinated collective motion in bird flocks and fish schools inspires algorithms for cohesive swarm robotics. This paper presents a position-based flocking model that achieves persistent velocity alignment without velocity sensing. By…
The most general local Markovian stochastic model is investigated, for which it is known that the evolution equation is the Fokker-Planck equation. Special cases are investigated where uncorrelated initial states remain uncorrelated.…