Multiplicity of Neutrally Stable Periodic Orbits with Coexistence in the Chemostat Subject to Periodic Removal Rate

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 39-59, February 2024.
Abstract. We identify a taxonomic property on the growth functions in the multispecies chemostat model which ensures the coexistence of a subset of species under periodic removal rate. We show that proportions of some powers of the species densities are periodic functions, leading to an infinity of distinct neutrally stable periodic orbits depending on the initial condition. This condition on the species for neutral stability possesses the feature to be independent of the shape of the periodic signal for a given mean value. We also give conditions allowing the coexistence of two distinct subsets of species. Although these conditions are nongeneric, we show in simulations that when these conditions are only approximately satisfied, the behavior of the solutions is close to that of the nongeneric case over a long time interval, justifying the interest of our study.