LIMIT CYCLES OF PERTURBED GLOBAL ISOCHRO-
NOUS CENTER
Zouhair Diab
Department of Mathematics and Computer Science, Larbi Tebessi University, 12002 Tebessa, Algeria.
E-mail:zouhair.diab@univ-tebessa.dz
ORCID:
Maria Teresa de Bustos
Department of Applied Mathematics. University of Salamanca, Casas del Parque, 2, 37008-Salamanca, Spain.
E-mail:tbustos@usal.es
ORCID:
Miguel Ángel López
SIDIS Research Group, Department of Mathematics, Institute of Applied Mathematics in Science and Engineering
(IMACI), Polytechnic School of Cuenca, University of Castilla-La Mancha, 16071 Cuenca, Spain.
E-mail:mangel.lopez@uclm.es
ORCID:
Raquel Martínez
SIDIS Research Group, Department of Mathematics, Institute of Applied Mathematics in Science and Engineering
(IMACI), Polytechnic School of Cuenca, University of Castilla-La Mancha, 16071 Cuenca, Spain.
E-mail:Raquel.Martinez@uclm.es
ORCID:
Reception: 29/08/2022 Acceptance: 13/09/2022 Publication: 29/12/2022
Suggested citation:
Zouhair D., Maria Teresa B. , Miguel Ángel L. and Raquel M.(2022). Limit cycles of perturbed global isochronous center. 3C
Tecnología. Glosas de innovación aplicada a la pyme,11 (2), 25-36. https://doi.org/10.17993/3ctecno.2022.v11n2e42.25-36
https://doi.org/10.17993/3ctecno.2022.v11n2e42.25-36
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed. 42 Vol. 11 N.º 2 August - December 2022
25
ABSTRACT
We apply the averaging method of first order to study the maximum number of limit cycles of the
ordinary differential systems of the form
¨x+x=ε(f1(x, y)y+f2(x, y)) ,
¨y+y=ε(g1(x, y)x+g2(x, y)) ,
where
f1
(
x, y
)and
g1
(
x, y
)are real cubic polynomials;
f2
(
x, y
)and
g2
(
x, y
)are real quadratic polynomials.
Furthermore εis a small parameter.
KEYWORDS
Limit Cycles, Averaging Method, Ordinary Differential Systems
https://doi.org/10.17993/3ctecno.2022.v11n2e42.25-36
1 INTRODUCTION AND STATEMENT OF THE MAIN RESULT
At the Paris International Congress of Mathematics in 1900, Hilbert presented twenty-three problems
in mathematics. Some problems are still unsolved so far, they were a challenge for all mathematicians
of that era. The second part of the well-known Hilbert’s 16th problem is to find the maximum number
of limit cycles and their position for an ordinary differential planar system of degree nof the form
˙x=ψ(x, y),
˙y=η(x, y),(1)
where
n
is a positive integer, the dot above the variables represents the first derivative with respect to
the variable
t
,
ψ
(
x