Agree it's not a circuit one would normally use as an oscillator, but will oscillate at the ~LC parallel resonance over a range of L & C. This will begin to oscillate with a voltage across the network of ~1.8V out to beyond ~8.5V, then hysteresis entered and it will not oscillate until the voltage drops to ~6.4V.
What's happening is as the DC voltage is increased to 1.8V the circuit exhibits enough effective negative R (-R) to kick off oscillations, once the oscillations start the the waveform swings above and below the DC set bias point. As the bias voltage approaches and increases beyond the point where the -R subsides (~ 6.4V) the waveform "swings" into the + R region, but enough of the waveform swings into the -R regions so the waveform cycle average is still effective -R. As the bias voltage increases eventually reaching ~8.5V where the waveform average is no longer -R (more into the +R region than the -R) and the waveform collapses and oscillation subsides. Dropping the bias voltage back towards zero, and ~6.4V oscillation start up again.
We've confirmed this behavior by measurement.
Anyway, interesting circuit with some interesting behavior, but maybe not very useful, and reminds of the chaotic oscillator based upon the Chua Diode
Best,