用第一近似法研究微分系统的完全振荡、旋转和徘徊特性

Pub Date : 2024-07-05 DOI:10.1134/s0001434624030313
I. N. Sergeev
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引用次数: 0

摘要

摘要 介绍了微分方程系统(关于其零解)的完全振荡、旋转和游走以及完全不振荡、不旋转和不游走的概念。这些性质与系统的相应特征之间建立了一一对应的关系。给出了使用第一近似系统研究这些特性的保证可能性的迹象,以及不可能使用第一近似系统的例子。
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Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation

Abstract

The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given.

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