Only run once circuit hits a certain voltage

I have a solar powered circuit charging some super capacitors. Once the supercapcitors reach a certain voltage, say 7V, I want it to power the arduino and rest of the system. Then when the voltage drops below 5V (the arduino wont function properly), it cut's power to the circuit until it reaches 7V again.

Can you point me in the right direction of what I should be researching. I imagine I'll need to trigger a transistor (or relay) with a diode that blocks current until it hits 7V. But I need the transistor to remain open until it drops below 5V.

You waste precious power by running the Arduino on 5-7 V. A better approach is to connect the supercap to Vcc (by passing or eliminating the regulator) and running on 5 or less volts.

Nick Gammon wrote an excellent tutorial on running an Arduino remote data node on a solar panel and a supercap. Also be sure to study his power saving tutorial.

I'm also running a 3G gsm module (requires most of the power). I'm yet to find one that will run on less than 5V like the GSM module did. Powersaving in incriments wont really help. It is a waste of power but as long as the sun is out I just need it to operate once every 15 or so minutes (using 500F supercaps)