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Full-Text Articles in Physical Sciences and Mathematics
Global Dynamics Of Triangular Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luis
Global Dynamics Of Triangular Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luis
Eduardo Cabral Balreira
We consider continuous triangular maps on IN, where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our results to competition …
Local Stability Implies Global Stability For The Planar Ricker Competition Model, Eduardo C. Balreira, Saber Elaydi, Rafael Luis
Local Stability Implies Global Stability For The Planar Ricker Competition Model, Eduardo C. Balreira, Saber Elaydi, Rafael Luis
Eduardo Cabral Balreira
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.