Kinetic theory of pattern formation in a generalized multi-species Vicsek model

The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained from single-species models. In this paper, we derive a kinetic theory for multi-species systems of self-propelled particles with (anti-)alignment interactions. We summarize the numerical results for the binary system before employing linear stability analysis on the coarse-grained system. We find good agreement between theoretical predictions and particle simulations, and our kinetic theory is able to capture the correct lengthscale in the emergent coexistence phases through a Turing-Hopf instability. Extending the kinetic framework to multi-species systems with cyclic alignment interactions, we recover precisely the same emergent ordering as corresponding simulations of the microscopic model. More generally, our kinetic theory provides an extensible framework for analyzing pattern formation and collective order in multi-species active matter systems.