82 citations · 753 across the 71 of their papers we have counts for
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Large-time behaviour for coupled systems of Lotka-Volterra-type Fokker-Planck equations
Giuseppe Toscani, Mattia Zanella
We study a system of Fokker-Planck equations recently introduced to describe the temporal evolution of statistical distributions of population densities with predator-prey interact…
Individual-Based Foundation of SIR-Type Epidemic Models: mean-field limit and large time behaviour
Giorgio Martalò, Giuseppe Toscani, Mattia Zanella
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious,…
Lotka-Volterra-type kinetic equations for interacting species
Andrea Bondesan, Marco Menale, Giuseppe Toscani +1
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model bui…
Supercritical Fokker-Planck equations for consensus dynamics: large-time behaviour and weighted Nash-type inequalities
Giuseppe Toscani, Mattia Zanella
We study the main properties of the solution of a Fokker-Planck equation characterized by a variable diffusion coefficient and a polynomial superlinear drift, modeling the formatio…
Impact of interaction forces in first order many-agent systems for swarm manufacturing
Ferdinando Auricchio, Massimo Carraturo, Giuseppe Toscani +1
We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by c…
Trends to equilibrium for a nonlocal Fokker-Planck equation
Ferdinando Auricchio, Giuseppe Toscani, Mattia Zanella
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of…
On a class of Fokker-Planck equations with subcritical confinement
G. Toscani, M. Zanella
We study the relaxation to equilibrium for a class linear one-dimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting fe…
Boltzmann-type models with uncertain binary interactions
Andrea Tosin, Mattia Zanella
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynam…