Final answer:
The system of government that Emperor Diocletian tried to establish is known as the Tetrarchy, which is Greek for 'rule of four'.
Step-by-step explanation:
The term that best describes the peculiar system of government that Emperor Diocletian tried to establish is Tetrarchy. The system of the Tetrarchy, stemming from the Greek meaning 'rule of four,' was a political innovation wherein four emperors ruled the Roman Empire concurrently, with the aim of providing more effective control and stability.
Diocletian introduced this system toward the end of the third century CE as a response to the Crisis of the Third Century, aiming to end the frequent changes in leadership that had destabilized the empire. The empire was divided into two halves, East and West, each governed by an Augustus and a subordinate Caesar who could succeed the former and recruit a new junior partner, though in practice, this ideal of orderly succession was achieved only once.