Passively active-actively passive mutual anticipation in a communicative swarm

In this study, the alternation of the passively active and actively passive attitudes is considered as the basic scheme of communication in a society-like system. We construct a model for swarming behavior based only on mutual anticipation implementing this basic scheme of communication, and we estimate a swarm as a mobile network consisting of mutual anticipation structures. In particular, we show that a mutual anticipation structure can be expressed as a fixed point with respect to equivalence classes in a network and that redundant connections in a mutual anticipation structure can contribute to generating and maintaining a robust and dynamic swarming behavior.