Tristable Phenomenon in a Predator–Prey System Arising from Multiple Limit Cycles Bifurcation
2020 ◽
Vol 30
(09)
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pp. 2050129
Keyword(s):
New Type
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In this paper, we consider a predator–prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator–prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator–prey systems.
2017 ◽
Vol 27
(03)
◽
pp. 1750043
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2018 ◽
Vol 264
(5)
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pp. 3559-3595
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Keyword(s):
2013 ◽
Vol 23
(10)
◽
pp. 1350164
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Keyword(s):
2011 ◽
Vol 16
(3)
◽
pp. 719-738
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1986 ◽
Vol 48
(2)
◽
pp. 137-148
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2013 ◽
Vol 2013
◽
pp. 1-8
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2007 ◽
Vol 2007
◽
pp. 1-15
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