Search for: All records

Abstract Recent advances in human mobility research have revealed consistent pairwise characteristics in movement behaviour, yet existing mobility models often overlook the spatial and topological structure of mobility networks. By analysing millions of devices' anonymized cell phone trajectories, we show that human mobility networks exhibit a pronounced polycentric and modular structure, in which movements within spatial modules differ fundamentally from movements between modules. This finding challenges the common assumption of uniform mobility dynamics across spatial scales. Inspired by switching behaviours in animal movement patterns, we introduce a ‘switch mechanism’ to distinguish intra-module and inter-module exploration modes. Incorporating this mechanism into a generative mobility model allows us to simultaneously reproduce individual-level mobility statistics and emergent network-level structures, including high modularity, long topological distances and frequent long-range travel. Our results provide a unified mechanistic explanation for the emergence of polycentric human mobility patterns and highlight the importance of scale-dependent movement dynamics, with implications for urban planning, transportation modelling and epidemic forecasting. 

Abstract We study a reaction–advection–diffusion model of a target–offender–guardian system designed to capture interactions between urban crime and policing. Using Crandall–Rabinowitz bifurcation theory and spectral analysis, we establish rigorous conditions for both steady-state and Hopf bifurcations. These results identify critical thresholds of policing intensity at which spatially uniform equilibria lose stability, leading either to persistent heterogeneous hotspots or oscillatory crime–policing cycles. From a criminological perspective, such thresholds represent tipping points in guardian mobility: once crossed, they can lock neighbourhoods into stable clusters of criminal activity or trigger recurrent waves of hotspot formation. Numerical simulations complement the theory, exhibiting stationary patterns, periodic oscillations and chaotic dynamics. By explicitly incorporating law enforcement as a third interacting component, our framework extends classical two-equation models. It offers new tools for analysing non-linear interactions, bifurcations and pattern formation in multi-agent social systems.