This I can confirm without a doubt.With war, it's all about casual traffic in your systems. Our systems with no traffic don't drop at all during a war, but others with traffic can plummet.
Nearly a year of tracking in a nominally low traffic area and Wars are virtually no problem for my systems because of nearly no traffic in the area.
Outside of the influence drops from Expansion, there is no "automated" influence effect on the BGS - EVERYTHING with influence changes are due to other players, so watch that traffic board to get a handle on how many go through and might affect influence.
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