An opinion formation model with dissipative structure

We propose an opinion formation model which includes both the influence of internal motivation and dissipation. Active agents adopt their neighbors’ opinions according to a simplified set of rules, but they may gradually lose their interests in the discussion and drop out of it. On the other hand, inert agents can become active by initial activation or internal motivation from neighbors, and participate in the discussion. The initial activation is usually due to occurrence of a social event. The internal motivation, opinion update and dissipation procedure take place simultaneously. We apply the voter rule in our model, and carry out analysis and numerical simulations. Results show if nonzero dissipation stays below a threshold value, the system evolves to a balance state where the average concentration of one opinion is equal to that of the other. With dissipation, a number of small-size opinion clusters exist in the end, but the system gains a fast relaxation rate. The final average opinion is closely related to the dissipation intensity and the length of time for initial activation.