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

Stability and oscillation properties of an arbitrary nonlinear differential system with the zero solution 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—concepts of measures of this probabilistic nature were introduced only recently. Relations between the values of various measures of the listed properties are studied.