On discrete Lotka-Volterra type models
The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation frequently used to describe the dynamics of biological systems in which two groups of species, predators and their preys interact. One of the basic results of the LV model is that under suitable conditions th...
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| Format: | Article |
| Language: | English |
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World Science Publishing Company
2012
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| Online Access: | http://irep.iium.edu.my/23712/ http://irep.iium.edu.my/23712/1/mfms-IJMP_CS%282012%29.pdf |
| _version_ | 1848779202149482496 |
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| author | Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation
frequently used to describe the dynamics of biological systems in which two groups of species,
predators and their preys interact. One of the basic results of the LV model is that under suitable
conditions the LV model can exhibit any asymptotical behavior such as equilibrium states,
periodic cycles, and attractors. The discrete analogy of LV model has been considered by many
researchers and has been called a quadratic LV model. In a discrete case, one of the unexpected
results is that a quadratic LV model cannot exhibit a periodic cycle. In this paper we study
nonlinear LV type models which include quadratic LV as a particular case. Unlike quadratic LV
models, LV type models can exhibit any asymptotical behavior such as equilibrium states,
periodic cycles, and attractors. |
| first_indexed | 2025-11-14T15:14:01Z |
| format | Article |
| id | iium-23712 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:14:01Z |
| publishDate | 2012 |
| publisher | World Science Publishing Company |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-237122012-12-28T06:27:02Z http://irep.iium.edu.my/23712/ On discrete Lotka-Volterra type models Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation frequently used to describe the dynamics of biological systems in which two groups of species, predators and their preys interact. One of the basic results of the LV model is that under suitable conditions the LV model can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors. The discrete analogy of LV model has been considered by many researchers and has been called a quadratic LV model. In a discrete case, one of the unexpected results is that a quadratic LV model cannot exhibit a periodic cycle. In this paper we study nonlinear LV type models which include quadratic LV as a particular case. Unlike quadratic LV models, LV type models can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors. World Science Publishing Company 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/23712/1/mfms-IJMP_CS%282012%29.pdf Mukhamedov, Farrukh and Saburov, Mansoor (2012) On discrete Lotka-Volterra type models. International Journal of Modern Physics: Conference Series, 9 (1). pp. 341-346. ISSN 2010-1945 http://www.worldscinet.com/ijmpcs/09/0901/open-access/S2010194512005405.pdf 10.1142/S2010194512005405 |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Saburov, Mansoor On discrete Lotka-Volterra type models |
| title | On discrete Lotka-Volterra type models |
| title_full | On discrete Lotka-Volterra type models |
| title_fullStr | On discrete Lotka-Volterra type models |
| title_full_unstemmed | On discrete Lotka-Volterra type models |
| title_short | On discrete Lotka-Volterra type models |
| title_sort | on discrete lotka-volterra type models |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/23712/ http://irep.iium.edu.my/23712/ http://irep.iium.edu.my/23712/ http://irep.iium.edu.my/23712/1/mfms-IJMP_CS%282012%29.pdf |