Circular and Elliptic Orbits in a Feedback-mediated Chemostat
نویسندگان
چکیده
A chemostat with two organisms competing for a single growthlimiting nutrient controlled by feedback-mediated dilution rate is analyzed. A specific feedback function is constructed which yields circular and elliptical periodic orbits for the limiting system. A theorem on the stabilization of periodic orbits in conservative systems is developed and for a given elliptical orbit, the result is used to modify the chemostat so that the chosen orbit is asymptotically stable. Finally, the feedback function is modified so that finitely many nested periodic orbits of alternating stability exist.
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