Document Type
Post-Print
Publication Date
7-2014
Abstract
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 models.
Identifier
10.1016/j.na.2014.03.019
Publisher
Elsevier Ltd.
Repository Citation
Balreira, E. C., Elaydi, S., & Luís, R. (2014). Global dynamics of triangular maps. Nonlinear Analysis: Theory, Methods & Applications, 104, 75-83. http://doi.org/10.1016/j.na.2014.03.019
Publication Information
Nonlinear Analysis: Theory, Methods & Applications