ﻻ يوجد ملخص باللغة العربية
IIn this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the chemoattractant is considered as a continuous signal which solves a diffusive equation. For this model we prove the mean-field limit in the Wasserstein distance to a system given by the coupling of a Vlasov-type equation with the chemoattractant equation. Our approach is not based on empirical measures and we show the limit with explicit bounds, by proving also existence and uniqueness for the limit system. In the monokinetic case we derive pressureless nonlocal Euler-type model with chemotaxis.
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a transport eq
In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit measure almost surely is a weak solution to the limiting nonlinear Fok
We propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.
In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions evolution. We explore the natural question of the large population limit with two approaches:
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel model. The model we study has the same entropy as the minimal Keller-S