We show the global stabilization of the chemostat with nonmonotonic growth, adding a new species as a "biological" control, in presence of different removal rates for each species. This result is obtained by an extension of the Competitive Exclusion Principle in the chemostat, for the case of two species with different removal rates and at least one nonmonotonic response.

We perform the mathematical analysis of a model describing interaction two species in chemostat, involving competition and mutualism, simultaneously. The is five-dimensional system differential equations with nonlinear growth functions. give comprehensive description dynamics by determining analytically existence local stability conditions all steady-states, considering large class rates. prove...

<p style='text-indent:20px;'>A model of two microbial species in a chemostat competing for single resource is considered, where one the competitors that produces toxin, which lethal to other competitor (allelopathic inhibition), itself inhibited by substrate. Using general growth rate functions species, necessary and sufficient conditions existence local stability all equilibria four-dime...

Continuous culture of Bacillus popilliae was achieved for the first time in a small chemostat. Initially, variable cell yields during steady-state chemostat growth led to a re-examination of growth rates in batch cultures. B. popilliae NRRL B-2309 and a wild strain were both found to be natural mixtures of three substrains characterized by different growth rates and colony morphologies and vary...

Competitive exclusion is proved for a discrete-time, size-structured, nonlinear matrix model of m-species competition in the chemostat. The winner is the population able to grow at the lowest nutrient concentration. This extends the results of earlier work of the first author [11] where the case m = 2 was treated.

An analysis is given of a mathematical model of two predators feeding on a single prey growing in the chemostat. In the case that one of the predators goes extinct, a global stability result is obtained. Under appropriate circumstances, a bifurcation theorem can be used to show that coexistence of the predators occurs in the form of a limit cycle.