Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect
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...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/847360 |
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| author | A. Brett M. R. S. Kulenović |
| author_facet | A. Brett M. R. S. Kulenović |
| author_sort | A. Brett |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-23fbe0d91eb3416f84feda760f6d3d16 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-23fbe0d91eb3416f84feda760f6d3d162025-02-03T01:12:55ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/847360847360Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee EffectA. Brett0M. R. S. Kulenović1Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USADepartment of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USAWe 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.http://dx.doi.org/10.1155/2015/847360 |
| spellingShingle | A. Brett 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 |
| title | Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect |
| title_full | Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect |
| title_fullStr | Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect |
| title_full_unstemmed | Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect |
| title_short | Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect |
| title_sort | basins of attraction for two species competitive model with quadratic terms and the singular allee effect |
| url | http://dx.doi.org/10.1155/2015/847360 |
| work_keys_str_mv | AT abrett basinsofattractionfortwospeciescompetitivemodelwithquadratictermsandthesingularalleeeffect AT mrskulenovic basinsofattractionfortwospeciescompetitivemodelwithquadratictermsandthesingularalleeeffect |