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.
Document Object Identifier (DOI)
Balreira, E.C., Elaydi, S., & Luís, R. (2014). Global dynamics of triangular maps. Nonlinear Analysis: Theory, Methods & Applications, 104, 75-83. doi:10.1016/j.na.2014.03.019
Nonlinear Analysis: Theory, Methods & Applications