ху * = B – x – | 1+qx²

Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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7. Fairen and Velarde (1979) considered a model for respiration in a bacterial culture. The
equations are
ху
х — В — х —
1+qx?
ху
ý = A –
1+qx?
where x and y are the levels of nutrient and oxygen, respectively, and A, B, q > 0 are
parameters. Investigate the dynamics of this model. As a start, find all the fixed points and
classify them. Then consider the nullclines and try to construct a trapping region. Can you find
conditions on A, B, q under which the system has a stable limit cycle? Use numerical integration,
the Poincare-Bendixson theorem, results about Hopf bifurcations or whatever else seems useful.
Transcribed Image Text:7. Fairen and Velarde (1979) considered a model for respiration in a bacterial culture. The equations are ху х — В — х — 1+qx? ху ý = A – 1+qx? where x and y are the levels of nutrient and oxygen, respectively, and A, B, q > 0 are parameters. Investigate the dynamics of this model. As a start, find all the fixed points and classify them. Then consider the nullclines and try to construct a trapping region. Can you find conditions on A, B, q under which the system has a stable limit cycle? Use numerical integration, the Poincare-Bendixson theorem, results about Hopf bifurcations or whatever else seems useful.
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