The state of many physical, biological and socio-technical systems evolves by combining
smooth local transitions and abrupt resetting events to a set of reference values. The …

The Vicsek model is a flocking model comprising simple point particles originally proposed
with metric interactions: particles align to neighbours within a radius. Later, topological …

The aim of this paper is to derive macroscopic equations for processes on large co-evolving
networks, examples being opinion polarization with the emergence of filter bubbles or other …

We study a process of\emph {averaging} in a distributed system with\emph {noisy
communication}. Each of the agents in the system starts with some value and the goal of …

The foraging problem asks how a collective of particles with limited computational,
communication and movement capabilities can autonomously compress around a food …

In this paper, we construct a mean-field discrete-time Markov process evolving on a compact
subset of ℝ d can be stabilized to an arbitrary target distribution that has a continuous …

We study the critical behavior of a probabilistic automata network whose local rule consists
of two subrules. The first one, applied synchronously, is a probabilistic one-dimensional …

Abstract Models of ordering dynamics allow us to understand natural systems in which an
initially disordered population homogenizes some traits via local interactions. The simplest …

In this paper we review some recent results dealing with the transition between microscopic
and macroscopic scales in different fields, including kinetic theory, cells movement in …

We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a
predator–prey system. The individuals of each species are localized over the sites of a …