2013/06/29 by Degond, Pierre, Herty, Michael, Liu, Jian-Guo · 1 citation
#Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1307.0093
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the transported quantity in the neighboring cells. A motivation is pedestrian dynamics in a small corridor where the propagation of people in a part of the corridor can be either left or rightgoing. Under the assumptions of propagation of chaos and mean-field limit, we derive a master equation and the corresponding meanfield kinetic and macroscopic models. Steady--states are computed and analyzed analytically and exhibit the possibility of multiple meta-stable states and hysteresis.