Local and global properties of nonautonomous dynamical systems and their application to competition models

被引：1
|
作者：
Ili'chev, VG
机构：
[1] Rostov State University,
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2003年 / 44卷 / 03期
关键词：
universality; semigroup; coarseness; sign-invariant matrices; competition; global stability;
D O I：
10.1023/A:1023816915603
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop the inheritance principle for local properties by the global Poincare mapping of nonautonomous dynamical systems. Namely, if a semigroup property is uniformly locally universal then it is enjoyed by the global Poincare mapping. In studying the global dynamics of competitors in a periodic medium, the crucial role is played by the multiplicative semigroup of the so-called sign-invariant matrices. We give geometric criteria for stability of equilibria (periodic solutions) in competition models.
引用
收藏
页码：490 / 499
页数：10
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