Originally Posted by
maui
Overthinking. It's a common fault.
It appears you are underthinking, a more common fault.
For "THR," the FCOM says "The autothrottle applies thrust to maintain the vertical speed required by the pitch mode."
This means that the airspeed and vertical speed are simultaneously affected by both the autothrottle (per the statement above) and the pitch channel, as it pitches to maintain airspeed in FLCH.
Like any physical system, the target speed is not held perfectly, but rather constantly overshot and corrected unless having had some time to settle down in completely smooth air.
Let's say the VS went below target. If the THR behavior as described above makes a correction for it, and bumps the thrust up a little, the airspeed wont be "locked" to the airspeed target but will go up a little bit, until the pitch channel in FLCH responds to that and pitches up, bringing the speed back down to target. AKA, the phugoid cycle.
While it's pitching up, what's happening to the VS? It's also going up, to which THR will respond by pulling the thrust back. That will also pull the speed back, causing FLCH to pitch down, reversing the original correction. As a result of this, the VS is below target, bringing us back to step one.
Hopefully you can see now, how one triggering event can cause both thrust and pitch channels to reverse themselves in responding to each other's responses. Just how much do these reversals have a potential to cause even bigger reversals next time around, and diverge in amplitude as more time passes and they keep feeding each other? Who knows, with the interaction of multiple overlaid cycles now we're entering the black magic world of imaginary numbers, Laplace transforms, and who knows what else.
Obviously it is a solved problem as the 777 is not known for anything like this happening. But this is what the issue is, in the first place.