Document Type

Article

Date of Original Version

10-28-2014

DOI

10.1155/2015/847360

Abstract

We consider the following system of difference equations:

χn+1 = χ2n/(B1χ2n + C1y2n), yn+1 = y2n/(A2 + B2χ2n + C2y2n), 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.

Creative Commons License

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

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