The ones in the photo look like doubles. Very pretty, but top-heavy. Years ago, I planted a patch in my lawn (well, under it, actually, and it took a lot of effort!) There were various colours and shapes, but all of them were beautiful double blooms, some even double doubles. They come up every year, but every year some of the heads have done just what yours have, and have to be cut off and put into short vases. It is because the stems are OK for ordinary single daffodil blooms, but too slender for thesefancy ones if the winds blows them about.
They would probably do better if they were surrounded by other plants to grow through for support. Perhaps you could either move them or plant something near them that would be bushy enough to hold them up and the right height to have the flowers hovering nicely above? I can't do that in the lawn!