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Abstract and Applied Analysis
Volume 2014, Article ID 157573, 11 pages
http://dx.doi.org/10.1155/2014/157573
Research Article

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

1School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South Africa
2School of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South Africa

Received 9 April 2014; Accepted 23 July 2014; Published 3 September 2014

Academic Editor: Igor Leite Freire

Copyright © 2014 S. M. Simelane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.