A Multispecies Cross-Diffusion Model for Territorial Development

We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing previously-published account for K groups instead of two groups. then analyze this and present novel variations. Our assumes that agents’ movement is biased random walk away from rival groups’ markings. All interactions between agents are indirect, mediated through the numerically demonstrate in system three groups, segregate certain parameter regimes. Starting discrete model, we formally derive continuum 2K convection–diffusion equations our model. These exhibit cross-diffusion due avoidance Both numerical simulations linear stability analysis system, find many same properties hold K-group two-group introduce variations one corresponding some being more timid than others, other threatening others. different patterns those found original systems each these variations, finding both variation exhibits phase transition.