Abstract <p> For a nonlinear differential system with a zero solution, measures of oscillation, wandering, and rotation (and properties opposite to them) are defined, which are responsible for the possibility of choosing at random an initial value close to zero in such a way that the perturbed solution has (or does not have) pre-determined oscillatory properties. The correctness of these definitions and the relationships between different measures are studied, including meaningful special cases. </p>