What is the behavior of circuit with multiple Q points?
Most devices have a single solution for the Q or operating point. e.g. NPN transistor (graph 1). 

However, there are a number of devices that exhibit a region of dynamic negative resistance  (dV/dI = -R). In this region you could have three Q points. (Graph 2) Q1 and Q3 would be deemed as 'stable' because in this region they behave as a normal resistance (increase voltage, increase current) . Q2 is unstable because it acts as an negative resistance.

Note that these regions are not actual negative resistance, only the slope (dV/dI) which is negative. This dynamic negative resistance is often used to cancel out the resistance of an LC circuit creating a high Q filter circuit or even an oscillator.

Probably the first device to have this characteristic was the screen grid tetrode valve (tube).