Instability Criteria for Vibrations of a Vortex Subject to a Gyro-force

Here we study the instability of the vortex motion caused by vortex velocity non-monotonous dependence of the friction force in the presence of a gyro-force. We demonstrate that even a weak gyro-force renders the condition for onset of instability more strict than for a vortex not subject to gyro-forces: either the friction force must exceed a threshold, or its non-monotonic velocity dependence must be a rather steep function.