Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge
2014 ◽
Vol 2014
◽
pp. 1-12
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Keyword(s):
A modified Leslie-Gower predator-prey system with two delays is investigated. By choosingτ1andτ2as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
2021 ◽
Vol 26
(1)
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pp. 72-92
Keyword(s):
2012 ◽
Vol 17
(4)
◽
pp. 379-409
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Keyword(s):
2013 ◽
Vol 23
(12)
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pp. 1350194
2012 ◽
Vol 2012
◽
pp. 1-28
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Keyword(s):
2009 ◽
Vol 19
(07)
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pp. 2283-2294
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Keyword(s):