Perturbation theory of the quadratic Lotka–Volterra double center
Keyword(s):
We revisit the bifurcation theory of the Lotka–Volterra quadratic system [Formula: see text] with respect to arbitrary quadratic deformations. The system has a double center, which is moreover isochronous. We show that the deformed system can have at most two limit cycles on the finite plane, with possible distribution [Formula: see text], where [Formula: see text]. Our approach is based on the study of pairs of bifurcation functions associated to the centers, expressed in terms of iterated path integrals of length two.
1991 ◽
Vol 44
(3)
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pp. 511-526
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2006 ◽
Vol 39
(26)
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pp. 8231-8255
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2009 ◽
Vol 19
(12)
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pp. 4117-4130
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2012 ◽
Vol 22
(11)
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pp. 1250272
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2006 ◽
Vol 16
(04)
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pp. 925-943
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2004 ◽
Vol 14
(12)
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pp. 4285-4292
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