Abstract:

 

In this talk, we investigate the effect of toxins on coexistence solutions of three

unstirred chemostat models. In part 1, we study the existence and stability of

positive equilibria of the two-species system by the degree theory and the

bifurcation theory. Moreover, the effect of the toxins is investigated by the

perturbation technique. The results show that stable coexistence solution can occur

with dynamic toxin production, which cannot occur with constant toxin production.

Biologically speaking, it implies that dynamically allocated toxin production is

sufficiently effective in the occurrence of coexisting.

In part 2, we study the uniqueness, multiplicity and stability of positive equilibria of

the unstirred chemostat model with plasmid and toxin. It turns out that positive

solutions to this model are governed by two limiting systems. Based on the analysis

of uniqueness and stability of positive solutions to two limiting systems, the exact

multiplicity and stability of coexistence solutions to this model are established by

means of the combination of the fixed-point index theory, bifurcation theory and

perturbation theory.