Emerging Spatiotemporal Patterns from Discrete Migration Dynamics of Heterogeneous Agents

We propose a discrete agent-based model to investigate the migration dynamics of heterogeneous individuals. Compatibility among agents of different types is expressed in terms of homophily parameters capturing the extent to which similar individuals are attracted to, or dissimilar individuals are repelled by, each other. Based on agent-based simulations, we establish the connection between emerging spatiotemporal patterns and the homophily parameters. Key results are presented in a novel phase diagram, which reveals a wide range of spatial patterns including the cell, worm, herd, amoeba, and swarm modes under the dynamic regime and the separation, ghetto, and integration modes under the stationary one. Our model thus provides a generalized framework encompassing both static equilibrium and nonstationary systems to investigate the impact of agent heterogeneity on population dynamics. We demonstrate potential applications of our model to social systems using sexual segregation of ungulate habitats as a case study.