This design wasn't exactly based on particular species of Cockatoo, but it more or less resembles the sulphur-crested cockatoo, yellow-crested cockatoo, or the Major Mitchell's cockatoo (without the color changing effect). To be honest, I didn't thoroughly study cockatoo species and anatomy before I work on this design, so I made several mistakes on my first version. It was Robert J. Lang who pointed out those mistakes and drove me into fixing them as much as I can.
There are still some anatomical imperfections about this final version, but from a design perspective, it's not a bad design at all. It has a fully closed 3D body, a 3D head, and a very efficient ERM-inspired layout. The idea of allocating the crests as middle flaps may sound crazy, but it turned out that doing so nicely balanced the outflow and also results in a very interesting folding sequence.
However, as mentioned, there's still room for improvement. Arguably the biggest issue is that I didn't make the color change at the crests and the layer distribution made it look like the crests are coming out from the back of the head (whereas they really all come from the front). Another structural issue is that I used a bird base to create the claws since I initially believe that cockatoos, like most birds, have a 3-to-1 claw formation, but only later did I learn that they actually have a 2-to-2 formation, and it's much harder to shape a bird base nicely into that formation. I would certainly do these differently should I revise this design.