Mean-Field Limit of a Microscopic Individual-Based Model Describing Collective Motions
نویسندگان
چکیده
منابع مشابه
Mean-field approximation for a limit order driven market model.
A mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that the evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It e...
متن کاملMean-field limit for the stochastic Vicsek model
We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number N of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coup...
متن کاملA pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit
A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment closure technique in kinetic theory under the assumption that the methylation level is locally concentrated. The new system is hyperbolic with linear convect...
متن کاملIndividual based and mean-field modeling of direct aggregation
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the first-order model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, tog...
متن کاملMean-Field Analysis of a Dynamical Phase Transition in a Cellular Automaton Model for Collective Motion
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity parameter, and a dynamical phase transition exhibiting spontaneous breaking of rotational symmetry occurs at a critical parameter value. The model is analyzed usi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2021
ISSN: 1776-0852
DOI: 10.1080/14029251.2015.996444