How did the management of Byzantium change in connection with the invasions of enemies?

The existing system of dividing the empire into provinces and dioceses was replaced by the system of a femic device. Fema is the territory on which a military unit (or fleet) was based. The troops stationed in the fema were fed and provided at the expense of the population of this fema. The Byzantine soldiers, most likely, kept their household and came to military training and gathered under the banners during the war.
The femme device was a response to a growing threat from neighbors. The femme device helped to cope with the external threat, right up to the conquest of Constantinople by the crusaders.