Three-dimensional population systems

被引：2
|
作者：
Ahmad, Shair [1 ]
Tineo, Antonio [2 ]
机构：
[1] Univ Texas San Antonio, Dept Math, San Antonio, TX 78249 USA
[2] Univ Los Andes, Fac Ciencias, Dept Matemat, Merida 5101, Venezuela
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2008年 / 9卷 / 04期
关键词：
Lotka-Volterra competitive systems; persistence; Poincare-Bendixson theorem;
D O I：
10.1016/j.nonrwa.2007.04.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the interaction matrix B of a three-dimensional population system. with positive determinant and we prove that the invariant Sigma(B) = (trace of B) x (sum of principal minors of B) - (determinant of B), characterizes the sign of the real parts of the eigenvalues of B. Secondly, we write this invariant in a convenient form for us, in order to find some classes of matrices B such that sign(Sigma(DB)) = sign(Sigma(B)) tor any diagonal matrix D with positive diagonal elements. Finally, we give three applications of this result concerning three-dimensional Population systems. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1607 / 1611
页数：5
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