Collective behavior of schooling fish in confined domain

Collective phenomena occur across nature, from insect swarms to bird flocks and fish schools. Fish schools are a typical example where collective dynamics emerge from individual-level interactions. Here we construct a model that integrates, under geometric confinement, phenomenological behavioral rules based on vision with hydrodynamic interactions based on the flows generated by swimming fish. Using a systematic approach to study the collective dynamics over the entire parameter space, we show that a new multi-stability phase emerges in which the group of fish intermittently switches between schooling and milling. We analyze the intermittency regime with multivariate Fokker-Planck equation and dimensionality reduction based on coarse-grained order parameters. We find that this intermittency regime is sensitive to both school size and confining strength, and will break into bistability under certain circumstance. We conclude by commenting on the extendibility of these techniques in studying general collective dynamics.