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In this paper, we study the noise-induced truth seeking for heterogeneous Hegselmann-Krause (HK) model in opinion dynamics. It has been proved that small noise could induce the group to achieve truth in homogeneous HK model; however, for the more practical heterogeneous HK model, the theoretical conclusion is absent. Here, we prove that small noise could also induce the group to achieve truth in heterogenous HK model, and, moreover, we first theoretically prove that large noise could drive some agents to deviate from the truth. These theoretical findings evidently reveal how the free information flow spreading in the media determines the social truth seeking.

Recently opinion dynamics has attracted increasing attention from researchers of various fields [

In social dynamics, how the social groups seek and achieve truth interests much studies. In [

The truth seeking model in [

In this paper, we completely establish the theoretical analysis for the truth seeking of heterogeneous HK model with noise. Similar to [

The rest of this paper is organized as follows: Section

Let

In system (

The definition of achieving truth for the noisy system (

Let

In [

Let

Let

Also, to demonstrate Theorem

Suppose

The key of the proof of Theorem

Let

It can be checked that, at moment

The proof of Lemma

Theorem

Suppose

In Theorem

Let

In this section, we provide some simulation results to demonstrate the effect of small and large noise on truth seeking. Theorem

The truth seeking of model (

The truth seeking of model (

The truth seeking of model (

In this paper, we investigated the noise-induced truth seeking of the heterogeneous HK model. Compared to the existing results about the homogeneous case, we completely revealed how the free information flow with different strength affects the truth seeking in the heterogeneous model. On the one hand we showed that noise with proper strength will almost surely bring the group to achieve the truth, while, on the other hand, we further proved that large noise, which implies drastic information perturbation, will make some agents deviate from the truth. These results not only reveal the role free information flow plays in the social truth seeking but also provide prospective intervention design for promoting the truth seeking of social group.

At last we want to have a further discussion for the order/disorder transition which appears in this paper. It can be clearly found that an order/disorder transition happens with the variation of noise strength. However, whether the transition is a critical or just a crossover phenomenon is yet unclear in this study. In [

No data were used to support this study.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by the General Plan of Scientific Research Project of Beijing Educational Committee and the National Natural Science Foundation (NNSF) of China (Grant no. 61304155).