This circuit type is sometimes referred to as a peaking current source. Why do you think this naming is used?
The “peaking current source” naming used for this circuit comes from the fact that it produces a narrow region for which the output is independent of the input current.
The output current has a narrow peak. How can you adjust the circuit to produce a much wider, flatter peak?
A design improvement that helps in increasing the range of the input current for which the output is constant (wider and flatter peak) consists of cascading two stabilized current source circuits.