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Certain types of active systems can be treated as an equilibrium system with excess non-conservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles interacting with each other with both…
With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Von Neuman's work on universal machines and the hardware development have allowed the simulation of dynamical systems through a large set of interacting agents. This is a bottom-up approach which tries to derive global properties of a…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
Logistic growth on a static heterogenous substrate is studied both above and below the drift-induced delocalization transition. Using stochastic, agent-based simulations the delocalization of the highest eigenfunction is connected with the…
We investigate the low-temperature dynamics of a simple stochastic model, introduced recently in the context of the physics of glasses. The slowest characteristic time at equilibrium diverges exponentially at low temperature. On smaller…
Analysing learning in Multi-Agent Reinforcement Learning (MARL) environments is challenging, in particular with respect to \textit{individual} decision-making. Practitioners frequently struggle to compare training runs due to the inherent…
We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective…
Collective motion in animal groups emerges from the interplay between individual variability and social coordination, yet connecting these scales quantitatively has remained a major challenge.Using high-resolution trajectories of schooling…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
Standard models of population dynamics focus on the the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the…
We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical…
The dynamics of fermionic many-body systems is investigated in the framework of Boltzmann-Langevin (BL) stochastic one-body approaches. Within the recently introduced BLOB model, we examine the interplay between mean-field effects and…
In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which…
The Boltzmann kinetic equation is obtained from an integro-differential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy,…
Understanding systems level behaviour of many interacting agents is challenging in various ways, here we'll focus on the how the interaction between components can lead to hierarchical structures with different types of dynamics, or…