{"title":"Method for Constructing Periodic Solutions of Nonlinear Differential Equations","authors":"V. M. Budanov","doi":"10.1134/s0012266124050021","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We justify an analytical method for constructing periodic solutions of nonlinear systems of\nordinary differential equations of polynomial type. Periodic solutions are constructed in the form\nof Fourier series in which the coefficients are polynomials depending on a parameter, which is not\nassumed to be small. Two examples are considered: the van der Pol equation and the Lorenz\nsystem.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124050021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We justify an analytical method for constructing periodic solutions of nonlinear systems of
ordinary differential equations of polynomial type. Periodic solutions are constructed in the form
of Fourier series in which the coefficients are polynomials depending on a parameter, which is not
assumed to be small. Two examples are considered: the van der Pol equation and the Lorenz
system.
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