2025/01/27 by Khatib, Mariam Al, Gounane, Said, Igbida, Noureddine +1
#34A12 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.16275
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population 1) must traverse a territory occupied by another (population 2), necessitating strategies to mitigate overcrowding caused by spatial limitations. To capture these interactions, we model population 1 using a linear transport equation, while population 2 is described by a granular diffusion model a la sandpile to represent its internal dynamics and tendency to decongest. Through numerical simulations, we explore how different movement strategies of the traversing population (population 1) - including directed motion towards a specific destination, internal dispersion to minimize crowding, and uniform dispersal across the space - affects the behavior of population 2.