I know this is old, but for the people who are still looking for information regarding this subject, this explanation is not complete and partially inaccurate.
First, there are 2 types of stability. Static stability and dynamic stability. It is true that stability comes from the current situation attitude (angle of attack), but it has different effects for different aircraft. And it is possible to have positive static stability but with dynamic instability. Case in point, 727's deep stall where it's attitude effectively locks the tail in a 'wind shadow.' It causes oscillating moments that don't exist outside of this flight profile.
Static stability has to do with the short period moments of the aircraft. An aircraft with positive static stability is said to have a forces acting to try and return the aircraft to trimmed flight at its trimmed alpha. A neutrally static aircraft will desire to hold the current alpha even after disturbed. An aircraft with relaxed static or unstable static stability will continue to increase its alpha in the direction opposite of the flight path. In other words, neutral static stability will not remain at 2 degrees of pitch attitude (theta) once the stick is released. Instead, it will maintain the pitch rate (theta dot) that it had when the stick was released. Static stability will never have a description of oscillating moments, instead it will describe what happens right here, right now if a momentary force acts upon the aircraft.
Dynamic stability is the stability of the aircraft in the long term. It describes what happens after a certain amount of time. A dynamically stable aircraft will have no or little oscillating moments and will dampen oscillations over time. It will follow a trend that is predictable. An aircraft with neutral dynamic stability will maintain its oscillations until acted upon, and then after, continue whatever oscillations remain. But an aircraft with negative dynamic stability will continue to have diverging oscillations, increasing in amplitude from its original orientation.
The following 9 conditions describe, by example, what will occur with static and dynamic stability are both taken into consideration:
Positive static stability with positive dynamic stability: Aircraft will immediately attempt to return to its trim condition and
will have oscillations that dampen out as the forces return to
Neutral static stability with positive dynamic stability: Aircraft will hold its current alpha and its pitch rate will remain
constant with regard to its current alpha and the oscillations from
the disturbance will slowly dampen out and return to equillibrium.
Negative static stability with positive dynamic stability (bit of a misnomer, explained below):
Aircraft will continue to
increase alpha and its pitch rate will increase. The misnomer is that
there will be no oscillations because there are no forces acting to
return the aircraft to its previous state in the long term. So this
technically can't exist. Airspeed will continue to decrease and drag
will continue to increase until it is more of a brick than a plane.
This is undesirable in fighter aircraft as if it enters a spin, any oscillations that could help exit the spin will quickly
dampen out and recovery will be nearly impossible. (with regards to
the lateral axis only)
Positive static stability with neutral dynamic stability: Aircraft will want to return to normal flight, its AoA will decrease,
and its pitch rate will reverse. But the aircraft will continue this
oscillation indefinitely if no corrective measures are taken.
Neutral static stability with neutral dynamic stability: Aircraft will want to continue to maintain it's current angle of
attack and any disturbances and oscillations for correcting forces
will continue to oscillate as they did before. It have epitrochoidal
Negative static stability with neutral dynamic stability (yes, this exists, and is what is common in some fighter aircraft):
Without corrective inputs in a timely manner, this will have an
oscillating period and will also continue to diverge from normal flight. This can be a good thing when trying to recover a
fighter from a spin as the oscillations will continue and the aircraft can be "rocked out." The F-16's deep stall behavior is very much described like
this, and can be described as a falling leaf. I have a video on this,
from a simulator called DCS World, here. In fact, in the video, you can also see that the longitudinal axis also suffers from neutral dynamic stability in this flight envelope. The switch I press at 1 min and 45 seconds overrides the computers maximum control surface deflection window and I can then "rock the plane out" by increasing the amplitude of the oscillations until the airflow over the control surfaces allows the computer to recover from the deep stall.
Positive static stability with negative dynamic stability: This is what you want when you want to make passenger planes into
vomit planes. The corrective forces acting on the plane cause it to
overshoot and the oscillations increase in amplitude. But the plane
is still trying to right itself in the short term.
Neutral static stability with negative dynamic stability: At this point, I don't know if there is a point in describing the
behavior because I think you might be able to get the gist. The plane will want to maintain its current alpha, but will then reverse, causing larger amplitudes of oscillation on each reversal. It might have 1 or 2 cycles before it completely
diverges from controllable flight. Not the characteristics you really
want to have in an aircraft.
Negative static stability with negative dynamic stability: Just pure chaos. Basically any orientation along the lateral
axis will have a 'butterfly effect' response and unpredictable
behavior. Forces put in to try and correct it will have an
oscillatory response that will increase in amplitude on the next
cycle, causing the need for a larger input to correct and the pattern
Currently studying flight dynamics as a hobbyist and with 2 years of engineering school. Current project is for model aircraft with a flight control computer to emulate an aircraft with negative static stability and neutral dynamic stability.
And, for references sake, so you can figure this out on your own in a sort of mental simulation: