Dynamics of a bio-reactor model with chemotaxis

Long time dynamics of solutions to a strongly coupled system of parabolic equations modeling the competition in bio-reactors with chemotaxis will be studied. In particular, we show that the dynamical system possesses a global attractor and that it is strongly uniformly persistent if the trivial steady state is unstable. Using a result of Smith and Waltman on perturbation of global attractors, we also show that the positive steady state is unique and globally attracting.  2002 Elsevier Science (USA). All rights reserved.