I'm thinking there were phugoids. Most of us probably built model or paper airplanes as kids, and we all probably all saw what happens when the tail comes off. Not a ride you'd want to take but a tuck under to an high frequency inverted stall which may have developed into a spin.
I'm suggesting that after losing its empennage, the plane entered an aerodynamically stable maneuver which had a constant rate of change with respect to several variables - Included among them would be increasing air density, decreasing weight, changing center of gravity, and others. It would be a complex differential equation with all those variables affecting the frequency and amplitude of the oscillations.
peekay's chart has a certain symmetry to it and although it is beyond my mathematical abilities, I think it could be modeled.