PERIODIC ORBITS AND INVARIANT CONES IN THREE-DIMENSIONAL PIECEWISE LINEAR SYSTEMS

被引：12
|
作者：
Carmona, Victoriano [1 ]
Freire, Emilio [1 ]
Fernandez-Garcia, Soledad [2 ]
机构：
[1] Univ Seville, Escuela Tecn Super Ingn, Dept Matemat Aplicada 2, Seville 41092, Spain
[2] Inria, Paris Rocquencourt Ctr, MYCENAE Project Team, F-78153 Le Chesnay, France
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 01期
关键词：
Piecewise linear systems; periodic orbits; invariant manifolds; half-Poincare maps; invariant cones; LIMIT-CYCLE BIFURCATION; DIFFERENTIAL-SYSTEMS;
D O I：
10.3934/dcds.2015.35.59
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We deal with the existence of invariant cones in a family of three-dimensional non-observable piecewise linear systems with two zones of linearity. We find a subfamily of systems with one invariant cone foliated by periodic orbits. After that, we perturb the system by making it observable and non-homogeneous. Then, the periodic orbits that remain after the perturbation are analyzed.
引用
收藏
页码：59 / 72
页数：14
相关论文
共 50 条
  • [1] Invariant manifolds of periodic orbits for piecewise linear three-dimensional systems
    Carmona, V
    Freire, E
    Ponce, E
    Torres, F
    IMA JOURNAL OF APPLIED MATHEMATICS, 2004, 69 (01) : 71 - 91
  • [2] Periodic orbits for perturbations of piecewise linear systems
    Carmona, Victoriano
    Fernandez-Garcia, Soledad
    Freire, Emilio
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (04) : 2244 - 2266
  • [3] On the Number of Invariant Cones and Existence of Periodic Orbits in 3-dim Discontinuous Piecewise Linear Systems
    Huan, Song-Mei
    Yang, Xiao-Song
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (03):
  • [4] Periodic sinks and periodic saddle orbits induced by heteroclinic bifurcation in three-dimensional piecewise linear systems with two zones
    Wang, Lei
    Li, Qingdu
    Yang, Xiao-Song
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 404
  • [5] Bifurcation of invariant cones in piecewise linear homogeneous systems
    Carmona, V
    Freire, E
    Ponce, E
    Torres, F
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2005, 15 (08): : 2469 - 2484
  • [6] Homoclinic orbits in three-dimensional continuous piecewise linear generalized Michelson systems
    Li, Zhengkang
    Liu, Xingbo
    CHAOS, 2022, 32 (07)
  • [7] Existence of Homoclinic Cycles and Periodic Orbits in a Class of Three-Dimensional Piecewise Affine Systems
    Wang, Lei
    Yang, Xiao-Song
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (02):
  • [8] Saddle-node bifurcation of invariant cones in 3D piecewise linear systems
    Carmona, Victoriano
    Fernandez-Garcia, Soledad
    Freire, Emilio
    PHYSICA D-NONLINEAR PHENOMENA, 2012, 241 (05) : 623 - 635
  • [9] Existence of periodic orbits and chaos in a class of three-dimensional piecewise linear systems with two virtual stable node-foci
    Wei, Zhouchao
    Zhu, Bin
    Escalante-Gonzalez, R. J.
    NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2021, 43
  • [10] Existence and Stability of Invariant Cones in 3-Dim Homogeneous Piecewise Linear Systems with Two Zones
    Huan, Song-Mei
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2017, 27 (01):
12345