构建非线性微分方程周期解的方法

Pub Date : 2024-09-11 DOI:10.1134/s0012266124050021

V. M. Budanov

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摘要

摘要我们论证了一种构建多项式类型非线性常微分方程系统周期解的分析方法。周期解是以傅里叶级数的形式构造的，其中的系数是取决于一个参数的多项式，而这个参数并不假定很小。我们考虑了两个例子：范德尔波尔方程和洛伦兹系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Method for Constructing Periodic Solutions of Nonlinear Differential Equations

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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