  A suspension of swimming microorganisms often generates a large-scale
convective pattern known as bioconvection. In contrast to the thermal
Rayleigh-Benard system, recent experimental studies report an emergence of
steady localized convection patterns and bistability near the onset of
instability in bioconvection systems. In this study, to understand the
underlying mechanisms and identify the roles of particle self-propulsion in
pattern formation, we theoretically and numerically investigate a model
bioconvection system in a two-dimensional periodic boundary domain. In doing
so, we extend a standard bioconvection model by introducing the equilibrium
density profile as an independent parameter, for which the particle
self-propulsion is treated as an independent dimensional parameter. Since the
large-scale vertical structure dominates in this system, we are able to
simplify the model by truncating the higher vertical modes. With this truncated
model, we analytically derived the neutrally stable curve and found that the
particle motility stabilizes the system. We then numerically analyzed the
bifurcation diagram and found the bistable structure at the onset of
instability. These findings, localization and bistability, are consistent with
experimental observations. We further examined the global structure of the
bistable dynamical system and found that the non-trivial unstable steady
solution behaves as an edge state that separates the basins of attractors.
These results highlight the importance of particle self-propulsion in
bioconvection, and more generally our methodology based on the dynamical
systems theory is useful in understanding complex flow patterns in nature.
