Is there some ways to get the features of a curve?

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Now, I have a group of data which describes objects' access counts per seconds. According to these data I get the curves of every object as follows. enter image description here

So I wander how can I get the features of every curve.

For curve A, there is a sharp change between phase1 and phase2, but in the whole lifetime the curve A is periodically stable.

For curve B, there is a sharp change between phase1 and phase2, and in the whole lifetime this curve is not stable.

On the other hand, the curve c is ALWAYS stable in the whole lifetime.

In brief, I need to classify these curve to stabilization, periodical stabilization and sharp change. Moreover, for periodical stabilization I need to get the period, and for sharp change, I need to know the sharp change occurred in which phase.

***************classes description********************

stabilization means the values of the curve are always around a certain value without great change. The curve C is a rough description.

periodical stabilization means the values of the curve have great change between two phase, and this kind of change is periodical. The curve A is a rough description.

sharp change means the values of the curve have great change between two phase and this kind of change is not repetitive. The curve B is a rough description.

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