Localization and bistability of bioconvection in a doubly periodic domain

TL;DR

This paper investigates how particle self-propulsion influences pattern formation in bioconvection within a doubly periodic domain, revealing localization and bistability phenomena consistent with experimental observations through theoretical and numerical analysis.

Contribution

It introduces an extended bioconvection model incorporating particle self-propulsion and equilibrium density, providing analytical and numerical insights into pattern localization and bistability.

Findings

Particle motility stabilizes the system.

Bistable structures emerge at the onset of instability.

Unstable steady solutions act as edge states separating attractors.

Abstract

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.