Abstract:
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.
Keywords:differential system, characteristic frequency, oscillation, wandering,
rotation, measure of oscillation, measure of wandering, measure of rotation.
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