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Abstract <p>Using specific examples, the paper proves that the presence of radial stability, asymptotic stability, or complete instability (of any type: Lyapunov, Perron, or upper-limit) properties of a non-one-dimensional autonomous nonlinear differential system, along each ray starting from zero, generally speaking, does not imply the presence of stability, asymptotic stability, or, accordingly, complete instability of the same type.</p>

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Examples of Differential Systems with Contrasting Combinations of Radial Stability and Instability

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • A. A. Bondarev

摘要

Abstract

Using specific examples, the paper proves that the presence of radial stability, asymptotic stability, or complete instability (of any type: Lyapunov, Perron, or upper-limit) properties of a non-one-dimensional autonomous nonlinear differential system, along each ray starting from zero, generally speaking, does not imply the presence of stability, asymptotic stability, or, accordingly, complete instability of the same type.