Could this airship be passively stabilized?

One of the main concept problems I found is the difficulty to keep the device at a constant height during the night (when solar energy is not available) without spending the scarce electric power stored in a lithium battery. With that issue I remembered a question I asked myself when I was a child and I wondered where did helium balloons go when you release them. Intuitively one could think that it will rise until due to the low outer pressure the balloon eventually explodes, or maybe the coldness of the atmosphere will cool the helium inside the balloon, it's density will rise and an equilibrium will be achieved (now I thing the balloon will just deflate and will fall down at it's limit speed).
I roughly modelized the behaviour of a balloon in an standard atmosphere. First if all I needed to measure how manometric pressure varies inside a balloon as function of its radius. It resulted in something curious, since I could really check how pressure was highest at a given radius, to drop at higher ones and finally keep rising smoothly. Here is the graph I've made.


Hard to modelise that, uh? But I don't need that peak at small radius, so I approximate that graph to a logaritmic function (since it tends to infinite but very slowly). Yes, not precise, but it's mission is just to say that the manometric pressure slightly grows with radius (with high ones). It's analytic expression is 458*ln(1000*x+1) and expressed in mmHg (which means multiplying by 760/101325) is something like that:



So, running a script in Python about the behaviour of a balloon initially filled with 1 kg. of helium at 101325 Pa and (and that's important) ignoring the friction the movement would be like that:
That's funny to see that the balloon would rise up and down all the time at great heights. That's counterintuitive, and probably wrong. That oscillatory movement due to balloon's inertia must be somehow stabilized (losing energy by friction), so an aerodynamic friction term (proportional to it's speed) will be added.


Now we can see how it tends to a stationary solution. No matter how the friction term is (subcritic or supercritic), since after some oscillations it will tend to the same solution. Now I don't care about the numeric results (since the pressure-ratio function was obtained with a common balloon that propably won't be the one used in the real airship), but it's interesting to check how some kind of passive stabilization exists. Now I have to check that all electronic devices will work at those temperatures (since many components won't work below -40ºC).