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
  • [31] Piecewise linear differential systems with only centers can create limit cycles?
    Jaume Llibre
    Marco Antonio Teixeira
    Nonlinear Dynamics, 2018, 91 : 249 - 255
  • [32] On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems
    Gouveia, Marcio R. A.
    Llibre, Jaume
    Novaes, Douglas D.
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 271 : 365 - 374
  • [33] Limit cycles in planar piecewise linear differential systems with nonregular separation line
    Cardin, Pedro Toniol
    Torregrosa, Joan
    PHYSICA D-NONLINEAR PHENOMENA, 2016, 337 : 67 - 82
  • [34] Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line
    Casimiro, Joyce A.
    Llibre, Jaume
    AXIOMS, 2024, 13 (03)
  • [35] Limit cycles for planar piecewise linear differential systems via first integrals
    Llibre J.
    Nuñez E.
    Teruel A.E.
    Qualitative Theory of Dynamical Systems, 2002, 3 (1) : 29 - 50
  • [36] Limit Cycles for a Class of Piecewise Smooth Quadratic Differential Systems with Multiple Parameters
    Bo, Xuekang
    Tian, Yun
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (10):
  • [37] Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems
    Llibre, Jaume
    Novaes, Douglas D.
    Zeli, Iris O.
    REVISTA MATEMATICA IBEROAMERICANA, 2020, 36 (01) : 291 - 318
  • [38] Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
    Llibre, Jaume
    Valls, Claudia
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2022, 37 (02): : 262 - 279
  • [39] On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones
    Silva Lima, Mauricio Firmino
    Pessoa, Claudio
    Pereira, Weber F.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (04):
  • [40] Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line
    da Cruz, Leonardo P. C.
    Torregrosa, Joan
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 514 (01)
12345