A study of a three-dimensional competitive Lotka–Volterra system
In this paper we will consider a community of three mutually competing species modeled by the Lotka–Volterra system: x˙i=xibi−∑i=13aijxj,i=1,2,3$$ {\left\{ {\dot x} \right._i} = {x_i}\left( {{b_i} - \sum\limits_{i = 1}^3 {{a_{ij}}{x_j}} } \right),i = 1,2,3 $$ where xi(t) is the population size of th...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2020-01-01
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| Series: | ITM Web of Conferences |
| Subjects: | |
| Online Access: | https://www.itm-conferences.org/articles/itmconf/pdf/2020/04/itmconf_icamnm2020_03010.pdf |
| _version_ | 1818969545622159360 |
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| author | Munteanu Florian |
| author_facet | Munteanu Florian |
| author_sort | Munteanu Florian |
| collection | DOAJ |
| description | In this paper we will consider a community of three mutually competing species modeled by the Lotka–Volterra system:
x˙i=xibi−∑i=13aijxj,i=1,2,3$$ {\left\{ {\dot x} \right._i} = {x_i}\left( {{b_i} - \sum\limits_{i = 1}^3 {{a_{ij}}{x_j}} } \right),i = 1,2,3 $$
where xi(t) is the population size of the i-th species at time t, Ẋi denote dxidt$${{dxi} \over {dt}}$$ and aij, bi are all strictly positive real numbers.
This system of ordinary differential equations represent a class of Kolmogorov systems. This kind of systems is widely used in the mathematical models for the dynamics of population, like predator-prey models or different models for the spread of diseases.
A qualitative analysis of this Lotka-Volterra system based on dynamical systems theory will be performed, by studying the local behavior in equilibrium points and obtaining local dynamics properties. |
| first_indexed | 2024-12-20T14:22:17Z |
| format | Article |
| id | doaj.art-649a908d4ed2432e9905367e7afb44aa |
| institution | Directory Open Access Journal |
| issn | 2271-2097 |
| language | English |
| last_indexed | 2024-12-20T14:22:17Z |
| publishDate | 2020-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ITM Web of Conferences |
| spelling | doaj.art-649a908d4ed2432e9905367e7afb44aa2022-12-21T19:37:54ZengEDP SciencesITM Web of Conferences2271-20972020-01-01340301010.1051/itmconf/20203403010itmconf_icamnm2020_03010A study of a three-dimensional competitive Lotka–Volterra systemMunteanu Florian0University of Craiova, Department of Applied Mathematics Al I Cuza 13In this paper we will consider a community of three mutually competing species modeled by the Lotka–Volterra system: x˙i=xibi−∑i=13aijxj,i=1,2,3$$ {\left\{ {\dot x} \right._i} = {x_i}\left( {{b_i} - \sum\limits_{i = 1}^3 {{a_{ij}}{x_j}} } \right),i = 1,2,3 $$ where xi(t) is the population size of the i-th species at time t, Ẋi denote dxidt$${{dxi} \over {dt}}$$ and aij, bi are all strictly positive real numbers. This system of ordinary differential equations represent a class of Kolmogorov systems. This kind of systems is widely used in the mathematical models for the dynamics of population, like predator-prey models or different models for the spread of diseases. A qualitative analysis of this Lotka-Volterra system based on dynamical systems theory will be performed, by studying the local behavior in equilibrium points and obtaining local dynamics properties.https://www.itm-conferences.org/articles/itmconf/pdf/2020/04/itmconf_icamnm2020_03010.pdfdynamical systemslotka-volterra systemsstability |
| spellingShingle | Munteanu Florian A study of a three-dimensional competitive Lotka–Volterra system ITM Web of Conferences dynamical systems lotka-volterra systems stability |
| title | A study of a three-dimensional competitive Lotka–Volterra system |
| title_full | A study of a three-dimensional competitive Lotka–Volterra system |
| title_fullStr | A study of a three-dimensional competitive Lotka–Volterra system |
| title_full_unstemmed | A study of a three-dimensional competitive Lotka–Volterra system |
| title_short | A study of a three-dimensional competitive Lotka–Volterra system |
| title_sort | study of a three dimensional competitive lotka volterra system |
| topic | dynamical systems lotka-volterra systems stability |
| url | https://www.itm-conferences.org/articles/itmconf/pdf/2020/04/itmconf_icamnm2020_03010.pdf |
| work_keys_str_mv | AT munteanuflorian astudyofathreedimensionalcompetitivelotkavolterrasystem AT munteanuflorian studyofathreedimensionalcompetitivelotkavolterrasystem |