  We model an enclosed system of bacteria, whose motility-induced phase
separation is coupled to slow population dynamics. Without noise, the system
shows both static phase separation and a limit cycle, in which a rising global
population causes a dense bacterial colony to form, which then declines by
local cell death, before dispersing to re-initiate the cycle. Adding
fluctuations, we find that static colonies are now metastable, moving between
spatial locations via rare and strongly nonequilibrium pathways, whereas the
limit cycle becomes almost periodic such that after each redispersion event the
next colony forms in a random location. These results, which hint at some
aspects of the biofilm-planktonic life cycle, can be explained by combining
tools from large deviation theory with a bifurcation analysis in which the
global population density plays the role of control parameter.
