I am not sure about young plants, but my mature ones have always started to die back after I've harvested the globes. I suppose, with no buds or fruit to support, there is a mechanism for the plant to shut off supplies to that stem and concentrate them on developing fresh shoots from the base. You should soon be able to see these shoots, and as yours are young plants, you leave them there so that they can produce globes for you next year.
You're lucky to find globes, however small, on young plants. I have a row of healthy looking young plants grown from seed in the spring, and they are supposed to have red globes. My plan is to transplant to a permanent position those that really are red, but there is no way to tell, yet. Artichokes don't come true from seed, so I need to keep on waiting, as I really fancy a row of red ones alongside a row of gree/purple ones.
