Document Type
Article
Date of Original Version
1-12-2015
Abstract
We consider the following system of difference equations: xn+1=xn2/B1xn2+C1yn2, yn+1=yn2/A2+B2xn2+C2yn2, n=0, 1,., where B1, C1, A2, B2, C2 are positive constants and x0, y0≥0 are initial conditions. This system has interesting dynamics and it can have up to seven equilibrium points as well as a singular point at (0,0), which always possesses a basin of attraction. We characterize the basins of attractions of all equilibrium points as well as the singular point at (0,0) and thus describe the global dynamics of this system. Since the singular point at (0,0) always possesses a basin of attraction this system exhibits Allee's effect.
Publication Title, e.g., Journal
Discrete Dynamics in Nature and Society
Volume
2015
Citation/Publisher Attribution
Brett, A., and M. R. Kulenović. "Basins of attraction for two-species competitive model with quadratic terms and the singular Allee effect." Discrete Dynamics in Nature and Society 2015, (2015). doi: 10.1155/2015/847360.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.