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

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