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

页码：59 / 97

页数：39

共 50 条

[1] On periodic orbits of polynomial relay systems
Jacquemard, Alain
Pereira, Weber Flavio
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2007, 17 (02) : 331 - 347
[2] On the continuation of degenerate periodic orbits in Hamiltonian systems
Meletlidou, E
Stagika, G
REGULAR & CHAOTIC DYNAMICS, 2006, 11 (01): : 131 - 138
[3] Continuation of periodic orbits in conservative and Hamiltonian systems
Muñoz-Almaraz, FJ
Freire, E
Galán, J
Doedel, E
Vanderbauwhede, A
PHYSICA D-NONLINEAR PHENOMENA, 2003, 181 (1-2) : 1 - 38
[4] Continuation of periodic orbits in symmetric Hamiltonian and conservative systems
Galan-Vioque, J.
Almaraz, F. J. M.
Macias, E. F.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2014, 223 (13): : 2705 - 2722
[5] Continuation of periodic orbits in symmetric Hamiltonian and conservative systems
J. Galan-Vioque
F. J. M. Almaraz
E. F. Macías
The European Physical Journal Special Topics, 2014, 223 : 2705 - 2722
[6] Examples of localization of periodic orbits of polynomial systems
Starkov, K
Coria, LN
2005 International Conference on Physics and Control (PHYSCON), 2005, : 606 - 609
[7] Continuation of Bifurcations of Periodic Orbits for Large-Scale Systems
Net, M.
Sanchez, J.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2015, 14 (02): : 674 - 698
[8] Continuation of periodic orbits in large-scale dissipative systems
Sánchez, J
Net, M
García-Archilla, B
Simó, C
EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS, 2005, : 625 - 630
[9] Continuation of relative periodic orbits in a class of triatomic Hamiltonian systems
James, Guillaume
Noble, Pascal
Sire, Yannick
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (04): : 1237 - 1264
[10] Localization of periodic orbits of polynomial systems by ellipsoidal estimates
Starkov, KE
Krishchenko, AP
CHAOS SOLITONS & FRACTALS, 2005, 23 (03) : 981 - 988

← 1 2 3 4 5 →