Anisotropic opinion dynamics with an adaptive social rule

We consider an anisotropic opinion formation process where the set of rules
B, that dictates what is the socially acceptable position, changes following the average voters' opinion. As in the case of a constant B, conservative (agreement with B) and liberal (agreement with neighbors) voters' attitudes are still represented by stable fixed points in the phase space of the system but with the difference that the conservative fixed point is stable for all possible values of the intervoter interaction. It has been also observed that, when the model is applied to sufficiently large populations, the time needed to consolidate a position in agreement with B is finite. We observed that there is also a range of values of the interaction where the two stable points coexist, opening the door for the modeling of bistability related phenomena, such as stochastic resonance and hysteresis.