According to the official Fabula Nova Crystallis mythology, the god Bhunivelze took control of the mortal world after banishing his mother Mwynn to the Unseen Realm. To find the gateway and take control of both realms, Bhunivelze created Pulse to search land, sea and sky for Etro's Gate. Etro was originally created to aid Pulse, but her similarity to Mwynn caused her to be discarded. To aid in his duty, Pulse created multiple fal'Cie before vanishing from the world. Since Pulse's departure, humans came to revere the deity and he was often identified as the "Maker".
Final Fantasy XIII
While the Pulse fal'Cie continued with their objective, the Lindzei fal'Cie who oversee Cocoon scheme to reveal Etro's Gate by the means of a mass sacrifice to bring back their creators. The Cocoon fal'Cie use Pulse l'Cie to see that goal through and when Anima brands Lightning, Snow, Sazh and Hope as its l'Cie, they and Vanille are brought before Pulse in a Historia Crux-like dimension, referred to as the gods' domain in the Ultimania. Emerging from his crystal, Pulse brands the l'Cie with its tendrils.
Lightning Returns: Final Fantasy XIII
Pulse is mentioned by Lightning and Fang when the latter states Pulse used the people of the world and threw them away similar to the way Lindzei treated the people of Cocoon and the Double Deity's description mentions Pulse's violent tyranny. Pulse appears during Lightning's battle with Bhunivelze, transformed into a half of a twin scythe for his creator to use. Pulse is presumably destroyed during the battle.
Final Fantasy Type-0/Agito
Pulse is the master of Arecia Al-Rashia and tasked her to find Etro's Gate in Orience by picking out twelve people from the Peristylium Suzaku and see if the quality of their souls is enough to become Agito and complete their task. Arecia created the crystals of Orience, as evidenced by their chosen l'Cie bearing the brand of Pulse. The crystals continue this function during the 600,104,971 cycles of war, which are spiritually depicted in Agito. The armistice in the the era of Type-0, the 600,104,972nd repeat of the cycle, was proclaimed by three of Orience's major nations as "in the name of the God Pulse", noted by Celestia quoting from the Fabula Conventions. During the coming of Finis, Class Zero, Arecia's chosen instruments, are given the option of becoming l'Cie to fight against the Lulusath Army. While in the previous cycles the twelve accepted the role, the present group refuses it and defeats the l'Cie Arbiter of Lulusath, freeing Orience from the cycle.