For stable head-flow characteristics the differential head - h - progressively falls with increasing flow rate - q.

For unstable head-flow characteristics the differential head - h - rises to a maximum and then progressively falls with increasing flow rate - q.

An unstable pump may start to oscillate between the two possible combinations of head-flow. The flow rate will modulate and the pipeline vibrate.
It is recommended that centrifugal pumps are designed and operated under stable conditions.