Basins of Attraction for Two Species Competitive Model with quadratic terms and the singular Allee Effect

Authors

Ann Brett, University of Rhode IslandFollow
Mustafa RS Kulenović, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

10-28-2014

Abstract

We consider the following system of difference equations:

χ_n+1 = χ²_n/(B₁χ²_n + C₁y²_n), y_n+1 = y²_n/(A₂ + B₂χ²_n + C₂y²_n), n = 0, 1, ..., where B₁, C₁, A₂, B₂, C₂ are positive constrants and χ0, 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.

Citation/Publisher Attribution

A. Brett and M. R. S. Kulenović, “Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect,” Discrete Dynamics in Nature and Society, vol. 2015, Article ID 847360, 16 pages, 2015.

Available at: http://dx.doi.org/10.1155/2015/847360

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.