When power's influence (bubbles) overlap?

[Strangepork]

Hello CMDRs,

Would someone be so kind as to explain what happens, in terms of control system benefits, to systems within the boundaries of two power's influence "bubbles" that are overlaping.

i believe LHS 262, near Nanoman is now one such system, for example.

With many thanks.

 

[Klab]

One bubble will go pop, the other bubble slowly get bigger until eventually it too ..goes...pop.