A general framework for validated continuation of periodic orbits in systems of polynomial ODEs | Zendy

Jan Bouwe van den Berg | Zendy; Elena Queirolo | Zendy

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A general framework for validated continuation of periodic orbits in systems of polynomial ODEs

Author(s) -

Jan Bouwe van den Berg,

Elena Queirolo

Publication year - 2020

Publication title -

journal of computational dynamics

Language(s) - English

Resource type - Journals

eISSN - 2158-2505

pISSN - 2158-2491

DOI - 10.3934/jcd.2021004

Subject(s) - continuation , ode , polynomial , generality , mathematical proof , dimension (graph theory) , vector field , mathematics , matlab , computer science , algebra over a field , mathematical analysis , pure mathematics , geometry , psychology , psychotherapist , programming language , operating system

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.

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