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Mathematical Medicine and Biology 1993 10(4):249-280; doi:10.1093/imammb/10.4.249
© 1993 by Institute of Mathematics and its Applications
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A mathematical analysis of the Grodins model of respiratory control

A. C. FLOWER, G. P. KALAMANGALAM and G. KEMBER

Mathematical Institute, University of Oxford 24–29 St Giles', Oxford OX1 3LB, UK
Department of Applied Mathematics, Technical University of Nova Scotia Halifax, Nova Scotia, Canada B3J 2X4

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.

Keywords: respiratory control; mathematical modelling; asymptotic analysis; delay recruitment equations; chaos


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