Circular and elliptic orbits in a feedback-mediated chemostat | Zendy

Willard S. Keeran | Zendy; Patrick De Leenheer | Zendy; Sergei S. Pilyugin | Zendy

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Circular and elliptic orbits in a feedback-mediated chemostat

Author(s) -

Willard S. Keeran,

Patrick De Leenheer,

Sergei S. Pilyugin

Publication year - 2007

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2007.7.779

Subject(s) - chemostat , limiting , orbit (dynamics) , function (biology) , stability (learning theory) , mathematics , control theory (sociology) , dilution , periodic orbits , mathematical analysis , physics , computer science , biology , engineering , thermodynamics , artificial intelligence , bacteria , mechanical engineering , control (management) , evolutionary biology , machine learning , aerospace engineering , genetics

A chemostat with two organisms competing for a single growth-limiting 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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