On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations

被引：1

作者：

Rezaiki, Nabil ^{[2
]}

Boulfoul, Amel ^{[1
]}

机构：

[1] 20 aout 1955 Univ, Dept Math, BP 26, Skikda 21000, Algeria

[2] Univ Badji Mokhtar, Dept Math, LMA Lab, POB 12, Annaba 23000, Algeria

来源：

JOURNAL OF APPLIED ANALYSIS | 2024年 / 30卷 / 01期

关键词：

Averaging theory; continuous and discontinuous differential system; isochronous center; limit cycle; PERIODIC-ORBITS; BIFURCATION; SYSTEMS;

D O I：

10.1515/jaa-2023-0018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the number of limit cycles bifurcated from the periodic orbits of a cubic uniform isochronous center with continuous and discontinuous quartic polynomial perturbations. Using the averaging theory of first order for continuous and discontinuous differential systems and comparing the obtained results, we show that the discontinuous systems have at least 6 more limit cycles than the continuous ones. This study needs some computations that have been verified using Maple.

引用

页码：35 / 50

页数：16

共 23 条

[1] Berezin I., 1964, COMPUTING METHODS, VII
[2] Averaging methods for finding periodic orbits via Brouwer degree
Buica, A
Llibre, J
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2004, 128 (01): : 7 - 22
[3] On Commuting Vector Fields and Darboux Functions for Planar Differential Equations
Choudhury, A. Ghose
Guha, Partha
[J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2013, 34 (03) : 212 - 226
[4] Conti R., 1994, LECT NOTES PURE APPL, V152, P21
[5] Debz N, 2022, MEM DIFFER EQU MATH, V86, P31
[6] Limit cycles of a class of planar polynomial differential systems
Debz, Nassima
Boulfoul, Amel
Berkane, Abdelhak
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (17) : 13592 - 13614
[7] DiBernardo M, 2008, APPL MATH SCI, V163, P1, DOI 10.1007/978-1-84628-708-4
[8] Han MA, 2015, J APPL ANAL COMPUT, V5, P809
[9] Hilbert D., 1900, 2 INT C MATH MP, P253
[10] On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems
Jiang, Ziguo
[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2016, 2016

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