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.
Global Dynamics of Triangular MapsNonlinear Analysis: Theory, Methods & Applications
Document Object Identifier (DOI)10.1016/j.na.2014.03.019
Citation InformationBalreira, 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