With the Twenty-two Dynasty of who governed the north from Bubastis, a period of foreign rulers started. The Twenty-four Dynasty was Ethiopians, while the Twenty-five Dynasty was Cushites. During this period, there were Ethiopian Kings from Napata struggling with the Assyrians for control over Egypt. In this same period, three groups (the Libyans, Kushites and some Egyptian families) ascended to the throne.
There are very few material remains that have been found for this period. The country was firmly reunited by the Twenty-two Dynasty founded by Shoshenq I in 945 BC (or 943 BC), who descended from Meshwesh immigrants, originally from Ancient Libya. This dynasty is also called the Libyan or the Bubastide Dynasty since it was founded by Libyans who lived in the Delta-city of Bubastis.
The early Bubastide Kings were powerful rulers able to re-establish Egyptian presence in Syria-Palestine. After the reign of Osorkon II, particularly, the country had effectively splintered into two states with Shoshenq III of the Twenty-Second Dynasty controlling Lower Egypt by 818 BC while Takelot II and his son Osorkon B (the future Osorkon III) ruling Middle and Upper Egypt.
In Thebes, a civil war engulfed the city between the forces of Pedubast, who had proclaimed himself Pharaoh versus the existing line of Libyan Dynasty of Osorkon III – Takelot III – Rudamun. This kingdom quickly fragmented after Rudamun's death with the rise of local city states under kings such as Peftjaubast of Herakleopolis, Nimlot of Hermopolis, and Ini at Thebes.
You can get more information here.