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The number of limit cycles bifurcating from the periodic orbits of an isochronous center
Author(s) -
Bey Meryem,
Badi Sabrina,
Fernane Khairedine,
Makhlouf Amar
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5385
Subject(s) - mathematics , annulus (botany) , quintic function , limit (mathematics) , center (category theory) , quartic function , bifurcation , limit cycle , homogeneous , mathematical analysis , infinite period bifurcation , periodic orbits , heteroclinic bifurcation , bifurcation theory , period doubling bifurcation , pure mathematics , physics , nonlinear system , combinatorics , chemistry , botany , quantum mechanics , biology , crystallography
This paper concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quintic homogeneous perturbations, at most 14 limit cycles birfucate from the period annulus of the considered system.