# American Institute of Mathematical Sciences

March  2014, 19(2): 323-351. doi: 10.3934/dcdsb.2014.19.323

## Local stability implies global stability for the planar Ricker competition model

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

Received  March 2013 Revised  July 2013 Published  February 2014

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.
Citation: E. Cabral Balreira, Saber Elaydi, Rafael Luís. Local stability implies global stability for the planar Ricker competition model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 323-351. doi: 10.3934/dcdsb.2014.19.323
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