Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations
The normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, whic...
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| Format: | Article |
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1324 |
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| author | Juan Francisco Sánchez-Pérez Manuel Conesa Iván Alhama Manuel Cánovas |
| author_facet | Juan Francisco Sánchez-Pérez Manuel Conesa Iván Alhama Manuel Cánovas |
| author_sort | Juan Francisco Sánchez-Pérez |
| collection | DOAJ |
| description | The normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, which is quite accurate, does not require complex mathematical steps; however, a deep physical understanding of the problem is required to choose the appropriate references to define the dimensionless variables. From the dimensionless groups derived, the functional dependences of some unknowns of interest are established. Due to the coupled nature of the problem that induces temporal concentration rates of each species that are quite different at each point of the phase diagram, this diagram has been divided into four stretches corresponding to the four quadrants. For each stretch, the limit values (maximum or minimum) of the variables, as well as their duration, are expressed in terms of the dimensionless groups derived before. Finally, to check all the mentioned dependences, a numerical simulation has been carried out. |
| first_indexed | 2024-03-10T17:45:10Z |
| format | Article |
| id | doaj.art-a671d6ed97aa4415b1f30839c840b296 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T17:45:10Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a671d6ed97aa4415b1f30839c840b2962023-11-20T09:35:12ZengMDPI AGMathematics2227-73902020-08-0188132410.3390/math8081324Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and ConcentrationsJuan Francisco Sánchez-Pérez0Manuel Conesa1Iván Alhama2Manuel Cánovas3Department of Applied Physics, Universidad Politécnica de Cartagena, 30203 Cartagena, SpainDepartment of Applied Physics, Universidad Politécnica de Cartagena, 30203 Cartagena, SpainDepartment of Mining and Civil Engineering, Universidad Politécnica de Cartagena, 30203 Cartagena, SpainDepartment of Metallurgical and Mining Engineering, Universidad Católica del Norte, Antofagasta 1240000, ChileThe normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, which is quite accurate, does not require complex mathematical steps; however, a deep physical understanding of the problem is required to choose the appropriate references to define the dimensionless variables. From the dimensionless groups derived, the functional dependences of some unknowns of interest are established. Due to the coupled nature of the problem that induces temporal concentration rates of each species that are quite different at each point of the phase diagram, this diagram has been divided into four stretches corresponding to the four quadrants. For each stretch, the limit values (maximum or minimum) of the variables, as well as their duration, are expressed in terms of the dimensionless groups derived before. Finally, to check all the mentioned dependences, a numerical simulation has been carried out.https://www.mdpi.com/2227-7390/8/8/1324Lotka–Volterra oscillatornon-dimensionalizationdimensionless groupsnumerical simulation |
| spellingShingle | Juan Francisco Sánchez-Pérez Manuel Conesa Iván Alhama Manuel Cánovas Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations Mathematics Lotka–Volterra oscillator non-dimensionalization dimensionless groups numerical simulation |
| title | Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations |
| title_full | Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations |
| title_fullStr | Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations |
| title_full_unstemmed | Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations |
| title_short | Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations |
| title_sort | study of lotka volterra biological or chemical oscillator problem using the normalization technique prediction of time and concentrations |
| topic | Lotka–Volterra oscillator non-dimensionalization dimensionless groups numerical simulation |
| url | https://www.mdpi.com/2227-7390/8/8/1324 |
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