PULSE Machines are strange devices used by Team Meteor in various places throughout the Reborn region. PULSE is an acronym, which stands for Pokémon Ultimation Link-System Exaggerata. The machine morphs into a Pokémon and amplifies its ability to incredible amounts, but also takes a severe toll on the Pokémon's body.
In battle, PULSE Machines act similar to Mega Evolution, requiring a held item and a PULSE owned by the trainer, but rather than the usual text, the game will say The foe's <x> mutated into PULSE <x>!
As revealed in Luminia's journal in Ametrine City, the first PULSE Machine was designed by her sister, Evelyn, to amplify her Magneton's healing powers in hope of helping her sister. Things escalated when Team Meteor heard about the creation and sought control of it, coming to a head when the Magneton evolved while still connected to the machine. The resulting effect fused the three together, creating ZEL.
Initially, PULSE Machines are only shown to have been used with Tangrowth to amplify their powers over flora. However, Taka explains to the player in Malchous Forest that they can be used on any species imaginable, a fact that becomes apparent as the player uncovers more of Team Meteor's schemes.