Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect
Keyword(s):
Blow Up
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We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology.
2021 ◽
Vol 26
(1)
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pp. 72-92
Keyword(s):
Bifurcation Analysis of a Delay-Induced Predator–Prey Model with Allee Effect and Prey Group Defense
2021 ◽
Vol 31
(10)
◽
pp. 2150158
Keyword(s):
Keyword(s):
2016 ◽
Vol 26
(10)
◽
pp. 1650165
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Keyword(s):
2013 ◽
Vol 23
(12)
◽
pp. 1350194