Related papers: Boltzmann-type equations for multi-agent systems w…
We propose a dynamical toy model of agents which possess a quantity and have an interaction radius depending on the amount of the quantity. They exchange the quantity with agents existing within their interaction radii. It is shown in the…
We introduce a class of one-dimensional linear kinetic equations of Boltzmann and Fokker--Planck type, describing the dynamics of individuals of a multi-agent society questing for high status in the social hierarchy. At the Boltzmann level,…
We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by recovering an equation of state for dense gases,…
A collection of $N$-diffusing interacting particles where each particle belongs to one of $K$ different populations is considered. Evolution equation for a particle from population $k$ depends on the $K$ empirical measures of particle…
Beyond specific settings, many multi-agent learning algorithms fail to converge to an equilibrium solution, instead displaying complex, non-stationary behaviours such as recurrent or chaotic orbits. In fact, recent literature suggests that…
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…
A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…
The individual-based models constitute a set of widely implemented tools to analyze the incidence of individuals heterogeneities in the spread of an infectious disease. In this work we focus our attention on human contacts heterogeneities…
In this work, we derive a system of Boltzmann-type equations to describe the spread of SARS-CoV-2 virus at the microscopic scale, that is by modeling the human-to-human mechanisms of transmission. To this end, we consider two populations,…
Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional…
It is shown that bifurcations of the mean-field dynamics of a Bose-Einstein condensate can be related with the quantum phase transitions of the original many-body system. As an example we explore the intra-band tunneling in the…
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 biology, chemotaxis, flocking phenomena and agent systems.…
This work addresses the synchronization/consensus problem of identical multi-agent system (MAS) where the agents' dynamics are linear and the communication network is arbitrarily switching among connected topologies. The approach uses a…
Time-varying hierarchical multi-agent systems are common in many applications. A well-known solution to control these systems is to use state feedback controllers that depend on the adjacency matrix to reach consensus. This solution has…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair…
The possibility of exploiting heterogeneous quantum systems to high precision, for storing, processing, and transmitting information makes them ideal candidates for multi-tasking purposes in quantum communication. Appropriate quantum…
Active-passive multiagent systems consist of agents subject to inputs (active agents) and agents with no inputs (passive agents), where active and passive agent roles are considered to be interchangeable in order to capture a wide array of…