Local stability implies global stability for the planar Ricker competition model
Open Access
- 1 January 2014
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 19 (2) , 323-351
Abstract
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.Keywords
This publication has 20 references indexed in Scilit:
- Bifurcation and invariant manifolds of the logistic competition modelJournal of Difference Equations and Applications, 2011
- Open problems in some competition modelsJournal of Difference Equations and Applications, 2011
- Dynamics of maps with nilpotent JacobiansJournal of Difference Equations and Applications, 2006
- Chaotic Dynamics in Two-Dimensional Noninvertible Maps1996
- A solution to the bidimensional Global Asymptotic Stability ConjectureAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 1995
- Asymptotic stability of linearizations of a planar vector field with a singular point implies global stabilityFunctional Analysis and Its Applications, 1995
- A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalizationAnnales Polonici Mathematici, 1995
- Some global bifurcations of two-dimensional endomorphisms by use of critical linesNonlinear Analysis, 1992
- Stability of discrete one-dimensional population modelsBulletin of Mathematical Biology, 1988
- Mappings with Non-Vanishing JacobianThe American Mathematical Monthly, 1971