2018/02/14 by Abdulaziz Alsenafi, Alethea Barbaro, Alethea B. T. Barbaro · 17 citations
Mathematics · Medicine · Physics and Astronomy · Psychology · #Convection #Diffusion #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Mechanics #Opinion Dynamics and Social Influence #Physics #Psychology #Statistical physics #Territoriality #Thermodynamics #math.DS #nlin.AO #nlin.CG #nlin.PS #physics.soc-ph
paper · pdf · open access · doi:10.1016/j.physa.2018.07.004
published in Physica A Statistical Mechanics and its Applications 510, 765-786 (Elsevier BV)
arxiv created 2018/02/14 · openalex publication_date 2018/07/05 · arxiv updated 2018/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an agent-based model to simulate gang territorial development motivated by graffiti marking on a two-dimensional discrete lattice. For simplicity, we assume that there are two rival gangs present, and they compete for territory. In this model, agents represent gang members and move according to a biased random walk, adding graffiti with some probability as they move and preferentially avoiding the other gang’s graffiti. All agent interactions are indirect, with the interactions occurring through the graffiti field. We show numerically that as parameters vary, a phase transition occurs between a well-mixed state and a well-segregated state. The numerical results show that system mass, decay rate and graffiti rate influence the critical parameter. From the discrete model, we derive a continuum system of convection–diffusion equations for territorial development. Using the continuum equations, we perform a linear stability analysis to determine the stability of the equilibrium solutions and we find that we can determine the precise location of the phase transition in parameter space as a function of the system mass and the graffiti creation and decay rates.