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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/157573 |
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| _version_ | 1832567947066867712 |
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| author | S. M. Simelane S. Abelman F. D. Duncan |
| author_facet | S. M. Simelane S. Abelman F. D. Duncan |
| author_sort | S. M. Simelane |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8513ba08ca564093b345b63f8beac453 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8513ba08ca564093b345b63f8beac4532025-02-03T01:00:10ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/157573157573Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect SpiracleS. M. Simelane0S. Abelman1F. D. Duncan2School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South AfricaSchool of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South AfricaSchool of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South AfricaThis 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.http://dx.doi.org/10.1155/2014/157573 |
| spellingShingle | S. M. Simelane S. Abelman F. D. Duncan Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle Abstract and Applied Analysis |
| title | Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle |
| title_full | Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle |
| title_fullStr | Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle |
| title_full_unstemmed | Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle |
| title_short | Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle |
| title_sort | dynamics of the oxygen carbon dioxide and water interaction across the insect spiracle |
| url | http://dx.doi.org/10.1155/2014/157573 |
| work_keys_str_mv | AT smsimelane dynamicsoftheoxygencarbondioxideandwaterinteractionacrosstheinsectspiracle AT sabelman dynamicsoftheoxygencarbondioxideandwaterinteractionacrosstheinsectspiracle AT fdduncan dynamicsoftheoxygencarbondioxideandwaterinteractionacrosstheinsectspiracle |