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<p>Stability and oscillation properties of an arbitrary nonlinear differential system with the&#xa0;zerosolution are studied: stability, asymptotic stability, complete instability (of various types: Lyapunov, Perron, and upper-limit),and complete wandering, oscillation, and rotation (as well as the corresponding opposite properties: nonwandering, nonoscillation, and nonrotation).For such a system, spherical and radial measures of these properties are defined—conceptsof measures of this probabilistic nature were introduced only recently.Relations between the values of various measures of the listed properties are&#xa0;studied.</p>

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Radial and Spherical Measures of Stability and Oscillation Properties of a Differential System

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • I. N. Sergeev

摘要

Stability and oscillation properties of an arbitrary nonlinear differential system with the zerosolution are studied: stability, asymptotic stability, complete instability (of various types: Lyapunov, Perron, and upper-limit),and complete wandering, oscillation, and rotation (as well as the corresponding opposite properties: nonwandering, nonoscillation, and nonrotation).For such a system, spherical and radial measures of these properties are defined—conceptsof measures of this probabilistic nature were introduced only recently.Relations between the values of various measures of the listed properties are studied.