Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615706 | Journal of Mathematical Analysis and Applications | 2014 | 13 Pages |
Abstract
In this paper, we study a two-dimensional piecewise smooth map arising in ecology. Such map, containing two parameters d and β, is derived from a model describing how masting of a mature forest happens and synchronizes. Here d is the energy depletion quantity and β is the coupling strength. Our main results are the following. First, we obtain a “weak” Sharkovskii ordering for the map on its nondiagonal invariant region for a certain set of parameters. In particular, we show that its Sharkovskii ordering is the natural number (resp., the positive even number) for β>1β>1 (resp., 0<β<10<β<1). Second, we obtain a region of parameter space for which its corresponding global dynamics can be completely characterized.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Chun-Ming Huang, Jonq Juang,