Higher order averaging theory for finding periodic solutions via Brouwer degree

By Jaume Llibre, Douglas Duarte Novaes, Marco Antonio Teixeira. 2014

161 citations recorded by the source corpus.

In this paper we deal with nonlinear differential systems of the form where for i = 0, 1, …, k, and are continuous functions, and T-periodic in the first variable, D being an open subset of , and ε a small parameter. For such differential systems, which do not need to be of class , under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/25f2e7803098858be7e897dc6e2d458051eb0a4e

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In Computational Theory and Mathematics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

A new result on averaging theory for a class of discontinuous planar differential systems with applications (2017, background): “The proof of Lemma 11 can be found in [16].”
Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones (2016, methodology): “As usual, the expressions of the higher order averaged functions are extensive (see [11, 15]), so we shall omit them here.”