The Lotka- Volterra competition models
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Nowadays, especially in the problem that dynamics has meaning, using of the mathematical models in the various sciences, is the important topic. Having employed the mathematical symbols for describing the obtained relation,one may find out a system of differential equations. In the present research,the Lotka-Volterra equations of models having n-species is studied. After classification it, the competition equation for said model in case of two species is analyzed. Finally, by linearization method, the stability of equilibrium points,stable and unstable manifolds for the above competition model will be analyzed.
Abstract
Nowadays, especially in the problem that dynamics has meaning, using of the mathematical models in the various sciences, is the important topic. Having employed the mathematical symbols for describing the obtained relation,one may find out a system of differential equations. In the present research,the Lotka-Volterra equations of models having n-species is studied. After classification it, the competition equation for said model in case of two species is analyzed. Finally, by linearization method, the stability of equilibrium points,stable and unstable manifolds for the above competition model will be analyzed.
참고문헌 (9)
- J. Hofbauer, "TThe Theory of Evolution and Dynamical Systems" (1988), Cambridge University Press
- T. Idema, "The Behaviour and Attractivness of The Lotka- Volterra Equations", pp.2006
- A.J. Lotka, "Elements of Mathematical Biology" (1956), Dover
- J. D. Murray, "Mathematical Biology, Volume I, An Introduction" (2002), Springer Verlag
- M.H. Rahmani Doust, "Analysis of a System of Coexistence Equations", Journal of Ultra Scientist of Physical Sciences, 19(1) (2007)
- M.H. Rahmani Doust, "TAnalysis of a System of Competition Equations", Journal of Ultra Scientist of Physical Sciences, 19(2) (2007)
- M.H. Rahmani Doust, "Analysis of a Predator-Prey Model with Interaspecies Coexistence", Journal of Ultra Scientist of Physical Sciences, 20(3) (2008)
- M.H. Rahmani Doust, "A Global Analysis of Lotka-Volterra Predator-Prey Model with Interaspecies Competition", Journal of Analysis and Computational, 4(1) (2008)
- V. Volterra, "Variations and Fluctuations of The Number of Individuals in Animal Species Living Together, In Animal ecology" (1931), Arno