Local stability implies global stability for the planar Ricker competition model
E. Cabral Balreira Saber Elaydi Rafael Luís
Discrete & Continuous Dynamical Systems - B 2014, 19(2): 323-351 doi: 10.3934/dcdsb.2014.19.323
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: compact invariant set critical curves fold cusp. global stability Competition model principal preimage function local stability

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