Noisy continuous-opinion dynamics

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals which lie in his area of confidence (including himself). In this work we study the effects of noise on this system. With certain probability, individuals are given the opportunity of change spontaneously their opinion to a random selected opinion inside the opinion space. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the moment opinion. We found that the interplay between opinion random jumps and confidence parameter induces interesting phenomena. Finally, using pattern formation techniques, we obtain approximated analytical results for critical conditions of opinion group formation

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