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Abstract <p> A dynamical system is considered in a sufficiently small neighborhood of its nondegenerate Lyapunov unstable equilibrium position. The existence of system trajectories localized in this neighborhood is discussed. An interesting phenomenon of a general nature takes place: when a perturbation is added to the right-hand sides of the equations, the singular point may disappear, but solutions occur that do not leave a small neighborhood of the original singular point. </p>

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Localization of Solutions of Ordinary Differential Equations near an Unstable Singular Point

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • E. I. Kugushev,
  • T. V. Salnikova

摘要

Abstract

A dynamical system is considered in a sufficiently small neighborhood of its nondegenerate Lyapunov unstable equilibrium position. The existence of system trajectories localized in this neighborhood is discussed. An interesting phenomenon of a general nature takes place: when a perturbation is added to the right-hand sides of the equations, the singular point may disappear, but solutions occur that do not leave a small neighborhood of the original singular point.