title: A mathematical analysis of the Grodins model of respiratory control.
abstract: The classical Grodins model of chemical respiratory control is analysed. Scaling and asymptotic analysis are used to reduce the model drastically to a much simplified form. In essence, the model consists of two separate controllers due to oxygen and carbon dioxide. The authors focus on the carbon dioxide controller, and show that it can be considered as two coupled delay recruitment equations. While, in normal circumstances, steady ventilation is stable, it is shown that, by varying controlling parameters, periodic and chaotic solutions may be obtained.
authors.affiliation: Mathematical Institute, University of Oxford, UK.
authors.forename: A C
authors.initials: AC
authors.lastname: Fowler
authors.forename: G P
authors.initials: GP
authors.lastname: Kalamangalam
authors.forename: G
authors.initials: G
authors.lastname: Kember
mesh_terms: D001921:Brain / Q000378:metabolism; D002245:Carbon Dioxide / Q000097:blood / Q000134:cerebrospinal fluid / Q000378:metabolism; D002302:Cardiac Output / Q000502:physiology; D002560:Cerebrovascular Circulation / Q000502:physiology; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D010100:Oxygen / Q000097:blood / Q000134:cerebrospinal fluid / Q000378:metabolism; D010507:Periodicity; D011659:Pulmonary Gas Exchange / Q000502:physiology; D012119:Respiration / Q000502:physiology*
chemical_list: D002245:Carbon Dioxide; D010100:Oxygen