That is phyllostachys aureosulcata yellow groove bamboo. As far as managing it, I would first suggest thinning out all of the dead culms, or some of the smaller old culms in order to reinvigorate the grove. That looks way too crowded. I think you need a lopper that cuts 2.5 inches, or one of those reciprocating saws to get the job done.

Along the barrier, I would also suggest cutting out the ones too close to the barrier 2-3ft, and severing a trench in there which can help prevent the root-boundedness of the grove.

I grow all of my bamboos without barriers, but I'm also far enough north where they don't run far enough each season to be a concern, and even if they did, it is pretty easy to rhizome prune since rhizomes don't grow very deep for at least all the species I grow.

Here is a link that might be useful: Some of my bamboos