Effects of allelochemicals produced by one population in a chemostat-like environment

In this paper, we study some general models suggested to describe the effects of chemical compounds produced by an algal population on its survival in a chemostat-like environment. The conditions for its persistence and extinction are found. In particular, in the first model we make very general assumptions to represent the uptake, the regulative and the inhibiting functions, and analyze its global stability completely. In the second one we specify the first two functions and leave general the third one. Here the regulative function has different property from that in the first model, and a saddle-node bifurcation phenomenon occurs. In addition, according to the experimental data reported in DellaGreca et al. [2010. Fatty acids released by Clorella vulgaris and their role in interference with Pseudokirchneriella subcapitata: experiments and modelling. J. Chem. Ecol. 36, 339-349], we present a further model in which a new inhibiting function gives rise to a complex dynamics. The three models exhibit different dynamical behaviors, in particular the number of positive equilibria associated with each model varies resulting one, two and three, respectively. We also point out that the main differences exhibited by these models result from different specializations of the regulative and the inhibiting functions.