Damage spreading transition in an opinion dynamics model

We study the damage spreading phenomena in two different ways in an opinion dynamics model introduced recently. This kinetic exchange type model is characterized by a fraction q of negative interactions and shows the presence of an order–disorder transition at qc. In the traditional method, two replicas of the population are considered in which the opinion of all the agents are identical initially, except for a single agent. The systems are then allowed to evolve identically. In the other method, the initial opinions are identical for all agents but the two replicas are evolved independently. In both cases, a damage spreading transition occurs at qd where 0.17<qd<0.18 in the traditional method and qd=0 for the other; the damage increases with q above qd and attains a constant value for q≥qc. However, the correlation between the evolved states above qc is clearly different in the two methods.