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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
World Science Publishing Company
2012
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| Subjects: | |
| Online Access: | 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 |
| Summary: | 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. |
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