Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator–Prey Models with Group Defense
2021 ◽
Vol 31
(10)
◽
pp. 2150154
Keyword(s):
For a family of two-dimensional predator–prey models of Gause type, we investigate the simultaneous occurrence of a center singularity and a limit cycle. The family is characterized by the fact that the functional response is nonanalytical and exhibits group defense. We prove the existence and uniqueness of the limit cycle using a new theorem for Liénard systems. The new theorem gives conditions for the uniqueness of a limit cycle which surrounds a period annulus. The results of this paper provide a mechanism for studying the global behavior of solutions to Gause systems through bifurcation of an integrable system which contains a center and a limit cycle.
Keyword(s):
Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
◽
pp. 1650204
◽
Keyword(s):
2002 ◽
Vol 35
(1)
◽
pp. 107-112
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2013 ◽
Vol 18
(5)
◽
pp. 708-716
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Keyword(s):