Their border would stop when the folks on the other side decide recognizing Israel and living peacefully with them is a viable survival strategy.

I expect Jordan, Egypt, Northern Lebanon, the new Syria and Saudi Arabia would have few real problems restraining themselves from overt activity.

Personally, I expect the following in the next few years:

* Egypt invades Libya.
* Hamas and/or Hezbollah cease to exist as an effective political / fighting force.
* Syria to fall under the control of the Muslim Brotherhood.
* Lebanon to be annexed by Turkey / Syria / Israel. It will cease to exist as separate political entity.
* Saudi Arabia / Iran go to war with the U.S. taking the Saudi side and China taking Iran's side. Russia will stay put and sell arms to everyone else in the region.
* Israel does NOT strike Iran. Really.