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Damage spreading transition in an opinion dynamics model

We study the damage spreading phenomena in two different ways in a 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 $q_c$. 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 $q_d$ where $q_d \approx 0.18$ in the traditional method and $q_d =0$ for the other; the damage increases with $q$ above $q_d$ and attains a constant value for $q\geq q_c$. However, the correlation between the evolved states above $q_c$ is clearly different in the two methods.