Abstract

This paper deals with an unstirred chemostat model of competitionbetween plasmid-bearing and plasmid-free organisms when theplasmid-bearing organism produces toxins. The toxins are lethal tothe plasmid-free organism, which leads to the conservationprinciple cannot be applied, and the resulting dynamical system isdescribed by three nonlinear partial differential equations and isnot monotone. First, the existence and multiplicity of thepositive steady-state solutions are determined by bifurcationtheory and degree theory. Second, the effects of the toxins areconsidered by perturbation technique. The results show that if theparameter $r$, which measures the effect of the toxins, issufficiently large, this model has at least two positive solutionsprovided that the maximal growth rate $a$ of $u$ lies in a certainrange; and has only a unique asymptotically stable positivesolution when $a$ belongs to another range.

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