Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle

This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect’s spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analys...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.1028-1038
Main Authors: Simelane, S. M., Duncan, F. D., Abelman, Shirley
Format: Article
Language:English
Subjects:
Analysis
Carbon dioxide
Colleges & universities
Differential equations
Equilibrium
Equilibrium (Physics)
Gases
Insects
Mathematical models
Oxygen
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Summary:This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect’s spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analysis is carried out in continuous time. The purpose of the research is to determine bounds for the gas volumes and to discuss the complexity and stability of the equilibria. Numerical simulations also demonstrate the dynamics of our model utilizing the new conditions for stability and instability.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/157573