Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions
A general population model with variable carrying capacity consisting of a coupled system of nonlinear ordinary differential equations is proposed, and a procedure for obtaining analytical solutions for three broad classes of models is provided. A particular case is when the population and carrying...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/2/3/27 |
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| author | M. Rodrigo D. Zulkarnaen |
| author_facet | M. Rodrigo D. Zulkarnaen |
| author_sort | M. Rodrigo |
| collection | DOAJ |
| description | A general population model with variable carrying capacity consisting of a coupled system of nonlinear ordinary differential equations is proposed, and a procedure for obtaining analytical solutions for three broad classes of models is provided. A particular case is when the population and carrying capacity per capita growth rates are proportional. As an example, a generalised Thornley–France model is given. Further examples are given when the growth rates are not proportional. A criterion when inflexion may occur is also provided, and results of numerical simulations are presented. |
| first_indexed | 2024-03-09T18:30:07Z |
| format | Article |
| id | doaj.art-351e31f5895b462d819546cb4102085b |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-09T18:30:07Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-351e31f5895b462d819546cb4102085b2023-11-24T07:33:09ZengMDPI AGAppliedMath2673-99092022-08-012346647910.3390/appliedmath2030027Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical SolutionsM. Rodrigo0D. Zulkarnaen1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, AustraliaDepartment of Mathematics, Universitas Islam Negeri Sunan Gunung Djati, Bandung 40614, IndonesiaA general population model with variable carrying capacity consisting of a coupled system of nonlinear ordinary differential equations is proposed, and a procedure for obtaining analytical solutions for three broad classes of models is provided. A particular case is when the population and carrying capacity per capita growth rates are proportional. As an example, a generalised Thornley–France model is given. Further examples are given when the growth rates are not proportional. A criterion when inflexion may occur is also provided, and results of numerical simulations are presented.https://www.mdpi.com/2673-9909/2/3/27population modelvariable carrying capacityexact solutionpower-law logisticlogisticGompertz |
| spellingShingle | M. Rodrigo D. Zulkarnaen Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions AppliedMath population model variable carrying capacity exact solution power-law logistic logistic Gompertz |
| title | Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions |
| title_full | Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions |
| title_fullStr | Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions |
| title_full_unstemmed | Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions |
| title_short | Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions |
| title_sort | mathematical models for population growth with variable carrying capacity analytical solutions |
| topic | population model variable carrying capacity exact solution power-law logistic logistic Gompertz |
| url | https://www.mdpi.com/2673-9909/2/3/27 |
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