The Lotka-Volterra canonical format

被引：18

作者：

Rocha, TA

Gléria, IM

Figueiredo, A

Brenig, L

机构：

[1] Univ Fed Alagoas, Dept Fis, BR-57072970 Maceio, AL, Brazil

[2] Univ Brasilia, Inst Fis, BR-70919970 Brasilia, DF, Brazil

[3] Free Univ Brussels, Serv Phys Stat Plasme & Opt Nonlineaire, B-1050 Brussels, Belgium

来源：

ECOLOGICAL MODELLING | 2005年 / 183卷 / 01期

关键词：

Lotka-Volterra; population dynamics; stability; first integrals;

D O I：

10.1016/j.ecolmodel.2004.07.023

中图分类号：

Q14 [生态学（生物生态学）];

学科分类号：

071012 ; 0713 ;

摘要：

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. (c) 2004 Elsevier B.V. All rights reserved.

引用

页码：95 / 106

页数：12

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