I think that would require E being in the middle in all phases of interaction between A and B, from connection initiation. That seems sufficient to set up two distinct synchronization regimes (A|B') and (A'|B) with E playing the fake roles. (It's a fascinating topic this auto-synchronizing chaotic system & I really need to read up on it: https://aip.scitation.org/doi/10.1063/1.4917383)