The Binary Pulsar System is a star system with neutron star and white dwarf in an unnamed galaxy. At the time that the Destiny was in the system the interaction between the two stars creates a deadly burst of gamma rays every 46 minutes, 37.4 seconds. As a result of the Lucian Alliance dialing in, Destiny dropped out of FTL in this system. These bursts of radiation started to overwhelm Destiny's shields as more and more of them hit and it took so much power to provide protection, the ship's Faster-Than-Light engine was down.
The bursts struck the top of the ship, so 90% of its shield power was diverted there. With the shields better able to protect Destiny, the FTL drive came back online, but Dr. Nicholas Rush diverted power away from the shields secretly so the drive would go back down and he could use the pulsars as leverage against the Lucian Alliance. Leveraging a blast that would completely collapse the shields and kill everyone except Rush, Eli Wallace, Chloe Armstrong and Adam Brody who were safe in the Hydroponics lab, Rush was able to force the Alliance forces to surrender rather than die and restored the shields again, allowing Destiny's FTL drive to come back online again and jump the ship away. There is a single planet within range of Destiny's Stargate from this system, but it was locked out as it was at extreme range to the Stargate. (SGU: "Incursion, Part 1", "Incursion, Part 2", "Intervention")