LOCAL STABILITY IMPLIES GLOBAL STABILITY FOR THE PLANAR RICKER COMPETITION MODEL

被引：37

作者：

Balera, E. Cabral ^{[1
]}

Elaydi, Saber ^{[1
]}

Luis, Rafael ^{[2
]}

机构：

[1] Trinity Univ, Dept Math, San Antonio, TX 78212 USA

[2] Univ Tecn Lisboa, Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Lisbon, Portugal

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 02期

关键词：

Competition model; local stability; global stability; critical curves; compact invariant set; principal preimage function; fold; cusp; BIFURCATION; MAPPINGS;

D O I：

10.3934/dcdsb.2014.19.323

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under certain analytic and geometric assumptions we show that local stability of the coexistence (positive) fixed point of the planar Ricker competition model implies global stability with respect to the interior of the positive quadrant. This result is a confluence of ideas from Dynamical Systems, Geometry, and Topology that provides a framework to the study of global stability for other planar competition models.

引用

页码：323 / 351

页数：29

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