The Lotka–Volterra canonical format

Most of the dynamical systems used in models of mathematical biology can be related to the simplest known model: the Lotka–Volterra (LV) system. Brenig (1988) showed that no matter the degree of nonlinearity of the considered model is often possible to relate it to a LV by a suitable coordinate tran...

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Bibliographic Details
Published in:Ecological modelling 2005-04, Vol.183 (1), p.95-106
Main Authors: Filho, Tarcísio M. Rocha, Gléria, Iram M., Figueiredo, Annibal, Brenig, Léon
Format: Article
Language:English
Subjects:
Animal, plant and microbial ecology
Biological and medical sciences
First integrals
Fundamental and applied biological sciences. Psychology
General aspects. Techniques
Lotka–Volterra
Methods and techniques (sampling, tagging, trapping, modelling...)
Population dynamics
Stability
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Summary:Most of the dynamical systems used in models of mathematical biology can be related to the simplest known model: the Lotka–Volterra (LV) system. Brenig (1988) showed that no matter the degree of nonlinearity of the considered model is often possible to relate it to a LV by a suitable coordinate transformation plus an embedding (Brenig, L., 1988. Complete factorization and analytic solutions of generalized Lotka–Volterra equations. Phys. Lett. A 133, 378–382). The LV system has then a status of canonical format. In this paper, we show how analytical properties of the original system can be studied from the dynamics of its associated LV. Our methodology is exemplified through the analysis of the stability of the interior fixed points and determination of conserved quantities.
ISSN:0304-3800
1872-7026
DOI:10.1016/j.ecolmodel.2004.07.023