On polynomial forms of nonlinear functional differential equations

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2021-01-01 DOI:10.3934/jcd.2021013

Olivier Hénot

引用次数: 10

Abstract

In this paper we study nonlinear autonomous retarded functional differential equations; that is, functional equations where the time derivative may depend on the past values of the variables. When the nonlinearities in such equations are comprised of elementary functions, we give a constructive proof of the existence of an embedding of the original coordinates yielding a polynomial differential equation. This embedding is a topological conjugacy between the semi-flow of the original differential equation and the semi-flow of the auxiliary polynomial differential equation. Further dynamical features are investigated; notably, for an equilibrium or a periodic orbit and its embedded counterpart, the stable and unstable eigenvalues have the same algebraic and geometric multiplicity.

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非线性泛函微分方程的多项式形式

本文研究了非线性自主时滞泛函微分方程;也就是说，在泛函方程中，时间导数可能依赖于变量的过去值。当非线性方程由初等函数组成时，我们给出了一个构造性证明，证明了原始坐标的嵌入产生多项式微分方程的存在性。这种嵌入是原始微分方程的半流与辅助多项式微分方程的半流之间的拓扑共轭。进一步研究了动力学特征;值得注意的是，对于平衡轨道或周期轨道及其嵌入对应物，稳定和不稳定特征值具有相同的代数和几何多重性。

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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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.