In aquatic microbial systems, high magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance ("apparent disappearance'') are relatively common. The authors suggest that, in order to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing of any kind, or external factors of any other nature, and can be caused by internal factors, and in particular by bacteria-phage interaction. Specifically, the authors suggest that the variations in abundance and the apparent disappearance phenomenon can be a result of phage infection and the lysis of infected bacteria. To illustrate this idea, the authors consider a reasonably simple mathematical model of bacteria-phage interaction based on the model suggested by Edoardo Beretta and Yang Kuang, which assumes neither periodic forcing, nor action of other external factors. The model admits a loss of stability via Andronov-Hopf bifurcation and exhibits dynamics which is able to explains the phenomenon. These properties of the model are especially distinctive for spatially non-homogeneous biosystems as well as biosystem with some sorts of cooperation or community effects.
doi:10.1017/S1446181120000085
Splitting of the separatrices after a Hamiltonian–Hopf bifurcation under periodic forcing
