A GENERAL FRAMEWORK FOR VALIDATED CONTINUATION OF PERIODIC ORBITS IN SYSTEMS OF POLYNOMIAL ODES

被引：8
|
作者：
van den Berg, Jan Bouwe [1 ]
Queirolo, Elena [2 ]
机构：
[1] Vrije Univ Amsterdam, Dept Math, Boelelaan 1081, NL-1081 HV Amsterdam, Netherlands
[2] Rutgers State Univ, Dept Math, 110 Frelinghusen Rd, Piscataway, NJ 08854 USA
来源：
JOURNAL OF COMPUTATIONAL DYNAMICS | 2021年 / 8卷 / 01期
关键词：
Validated numerics; periodic orbits; continuation; solution branch; polynomial ODEs; BIFURCATION DIAGRAM; RIGOROUS NUMERICS; EQUATION;
D O I：
10.3934/jcd.2021004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper a parametrized Newton-Kantorovich approach is applied to continuation of periodic orbits in arbitrary polynomial vector fields. This allows us to rigorously validate numerically computed branches of periodic solutions. We derive the estimates in full generality and present sample continuation proofs obtained using an implementation in Matlab. The presented approach is applicable to any polynomial vector field of any order and dimension. A variety of examples is presented to illustrate the efficacy of the method.
引用
收藏
页码：59 / 97
页数：39
相关论文
共 50 条
  • [31] PERIODIC ORBITS OF SINGULAR RADIALLY SYMMETRIC SYSTEMS
    Li, Shengjun
    Li, Wulan
    Fu, Yiping
    JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2017, 22 (03) : 393 - 401
  • [32] On periodic orbits and resonance in extrasolar planetary systems
    John D. Hadjidemetriou
    Celestial Mechanics and Dynamical Astronomy, 2008, 102 : 69 - 82
  • [33] No periodic orbits for the type A Bianchi’s systems
    Claudio A. Buzzi
    Jaume Llibre
    Journal of Nonlinear Mathematical Physics, 2015, 22 : 170 - 179
  • [34] On periodic orbits and resonance in extrasolar planetary systems
    Hadjidemetriou, John D.
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2008, 102 (1-3) : 69 - 82
  • [35] No periodic orbits for the type A Bianchi's systems
    Buzzi, Claudio A.
    Llibre, Jaume
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2015, 22 (02) : 170 - 179
  • [36] On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori
    Penati, T.
    Sansottera, M.
    Danesi, V.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 61 : 198 - 224
  • [37] Computation of periodic solution bifurcations in odes using bordered systems
    Doedel, EJ
    Govaerts, W
    Kuznetsov, YA
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (02) : 401 - 435
  • [38] A new method to compute periodic orbits in general symplectic maps
    Calleja, R.
    del-Castillo-Negrete, D.
    Martinez-del-Rio, D.
    Olvera, A.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 99 (99):
  • [39] Periodic Orbits of Nonlinear First-Order General Periodic Boundary Value Problem
    Wang, Feng
    Zhang, Fang
    Zhu, Hailong
    Li, Shengjun
    FILOMAT, 2016, 30 (13) : 3427 - 3434
  • [40] Maximum number of periodic orbits in parallel dynamical systems
    Aledo, Juan A.
    Diaz, Luis G.
    Martinez, Silvia
    Valverde, Jose C.
    INFORMATION SCIENCES, 2018, 468 : 63 - 71
12345