Competition and persistence of microorganisms in the gradostat - Tambulea, Adela (2005)
In the present thesis we give some answers to the question of which species of microorganisms can coexist and which can not in a spacial heterogeneous environment, called a gradostat. The dynamics of m species in n gradostat vessels is described by a system of mn ordinary differential equations. Using the results on the coexistence of two species, with the aid of the method of lower and upper solutions for systems with quasimonotone reaction terms, we are able to give general sufficient conditions for the persistence of n species in m vessels. For the case of 3 species, we are able to improve these conditions and construct a positively invariant region corresponding to each species concentration remaining strictly positive. For this we first look for conditions a species would need to fulfill in order to survive when introduced into a gradostat already containing two species at two-species persistent equilibrium concentration levels. Moreover, through a bifurcation analysis we can partially describe the region in the parameter space corresponding to persistence, and give numerous numerical examples of coexistence when our sufficient persistence conditions are fulfilled.
Keywords: Hochschulschrift