Local stability implies global stability for the planar Ricker competition model

E. Cabral Balreira; Saber Elaydi; Rafael Luís

doi:10.3934/dcdsb.2014.19.323

Article Contents

2014, Volume 19, Issue 2: 323-351. Doi: 10.3934/dcdsb.2014.19.323

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Local stability implies global stability for the planar Ricker competition model

1.
Department of Mathematics, Trinity University, San Antonio, Texas
2.
Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, Technical University of Lisbon, Lisbon

Received: February 28, 2013

Revised: June 30, 2013

Published: February 2014

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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.

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Mathematics Subject Classification: Primary: 39A30, 30A60; Secondary: 57R70.

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