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.
Document Object Identifier (DOI)
American Institute of Mathematical Sciences
Balreira, E.C., Elaydi, S., Luís, R. (2014). Local stability implies global stability for the planar Ricker competition model. Discrete and Continuous Dynamical Systems - Series B, 19(2), 323-351. doi:10.3934/dcdsb.2014.19.323
Discrete and Continuous Dynamical Systems - Series B