Limit Cycles of Polynomially Integrable Piecewise Differential Systems

被引：1
|
作者：
Garcia, Belen [1 ]
Llibre, Jaume [2 ]
del Rio, Jesus S. Perez [1 ]
Perez-Gonzalez, Set [1 ]
机构：
[1] Univ Oviedo, Dept Matemat, Avda Calvo Sotelo s n, Oviedo 33007, Spain
[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain
来源：
AXIOMS | 2023年 / 12卷 / 04期
基金：
欧盟地平线“2020”;
关键词：
algebraic limit cycle; piecewise differential system; polynomial integrable systems; NUMBER;
D O I：
10.3390/axioms12040342
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals.
引用
收藏
页数：19
相关论文
共 50 条
  • [1] Hopf bifurcation of limit cycles by perturbing piecewise integrable systems
    Han, Maoan
    Lu, Wen
    BULLETIN DES SCIENCES MATHEMATIQUES, 2020, 161
  • [2] The limit cycles of a class of piecewise differential systems
    Imane Benabdallah
    Rebiha Benterki
    Jaume Llibre
    Boletín de la Sociedad Matemática Mexicana, 2023, 29
  • [3] The limit cycles of a class of piecewise differential systems
    Benabdallah, Imane
    Benterki, Rebiha
    Llibre, Jaume
    BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2023, 29 (03):
  • [4] LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH INTEGRABLE DIFFERENTIAL SYSTEMS
    Yang, Jihua
    Zhao, Liqin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (06): : 2417 - 2425
  • [5] LIMIT CYCLES OF THE DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS ON THE CYLINDER
    Li, Jie
    Llibre, Jaume
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2022, 12 (03): : 952 - 963
  • [6] LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS
    Cardin, Pedro Toniol
    De Carvalho, Tiago
    Llibre, Jaume
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2011, 21 (11): : 3181 - 3194
  • [7] Limit Cycles of Continuous Piecewise Smooth Differential Systems
    Casimiro, Joyce A.
    Llibre, Jaume
    RESULTS IN MATHEMATICS, 2023, 78 (05)
  • [8] Algebraic Limit Cycles in Piecewise Linear Differential Systems
    Buzzi, Claudio A.
    Gasull, Armengol
    Torregrosa, Joan
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (03):
  • [9] ON LIMIT CYCLES OF PIECEWISE DIFFERENTIAL SYSTEMS AND A CLASS OF QUADRATIC SYSTEMS
    Berbache, Aziza
    Anasser, El
    MATHEMATICA BOHEMICA, 2022,
  • [10] The limit cycles of a class of discontinuous piecewise differential systems
    Baymout, Louiza
    Benterki, Rebiha
    Llibre, Jaume
    INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2024, 13 (04)
12345