Title
The Structure of ω-Limit Sets of Asymptotically Non-Autonomous Discrete Dynamical Systems
Document Type
Article
Publication Date
3-2020
Abstract
We consider a discrete non-autonomous semi-dynamical system generated by a family of continuous maps defined on a locally compact metric space. It is assumed that this family of maps uniformly converges to a continuous map. Such a non-autonomous system is called an asymptotically autonomous system. We extend the dynamical system to the metric one-point compactification of the phase space. This is done via the construction of an associated skew-product dynamical system. We prove, among other things, that the omega limit sets are invariant and invariantly connected. We apply our results to two populations models, the Ricker model with no Allee effect and Elaydi-Sacker model with the Allee effect, where it is assumed that the reproduction rate changes with time due to habitat fluctuation.
Identifier
85076400912 (Scopus)
DOI
10.3934/dcdsb.2019195
Publisher
American Institute of Mathematical Sciences
ISSN
15313492
Repository Citation
D'Aniello, E., & Elaydi, S. (2020). The structure of ω-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete and Continuous Dynamical Systems - Series B, 25(3), 903-915. http://doi.org/10.3934/dcdsb.2019195
Publication Information
Discrete and Continuous Dynamical Systems - Series B