Well, Mimosa pudica is a creeping plant, but that's not what yours is doing, yours looks as if its been too far away from a window without sufficient light, and what it's doing is reaching forward to get to the light. You've not said you're growing it indoors, but if you are, it needs a much brighter position - they like bright light,and a little sun in the morning or evening is fine.

Sensitive plants are floppy small bushes, which normally trail a little, but this one looks like it isn't getting enough light, as Bamboo says.

I agree. to make it produce side shoots cut the growing tip off say and Inch or so. that will stimulate side shoot development.

I used to have these at work. fantastic plants.