Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect
2015 ◽
Vol 2015
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pp. 1-16
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Keyword(s):
We consider the following system of difference equations:xn+1=xn2/B1xn2+C1yn2, yn+1=yn2/A2+B2xn2+C2yn2, n=0, 1, …, whereB1,C1,A2,B2,C2are positive constants andx0, y0≥0are 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.
2017 ◽
Vol 27
(08)
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pp. 1750128
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Keyword(s):
2018 ◽
Vol 28
(12)
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pp. 1850151
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Keyword(s):
2020 ◽
Vol 30
(16)
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pp. 2050239
2021 ◽
Vol 31
(11)
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pp. 2150168