The Robust Consensus of a Noisy Deffuant-Weisbuch Model
The Robust Consensus of a Noisy Deffuant-Weisbuch Model
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DOI：
10.1155/2018/1065451
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发表时间：
2018-12
影响因子：
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通讯作者：
Jiangbo Zhang;Yiyi Zhao
中科院分区：
文献类型：
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作者：
Jiangbo Zhang;Yiyi Zhao
我们构造了一种新的有外部噪声干扰的Deffuant-Weisbuch模型的意见形成，其中有有限的n个代理，并且演化是离散的。意见交互在每个时间步由一个随机选择的对发生。与原始Deffuant-Weisbuch模型的不同之处在于，任何选定对的通信都会受到噪声的影响。本文的目的是研究这个带有噪声的Deffuant-Weisbuch型模型的稳健一致性。我们首先将噪声强度定义为最大噪声绝对值。证明了当噪声强度小于某一阈值时，当t足够大时，该噪声模型将达到T-稳健一致；其次，我们证明了该噪声模型以正的概率达到稳健一致；最后，我们证明了这些结果，并给出了噪声强度与一些模型参数之间的数值关系。
We construct a new opinion formation of the Deffuant-Weisbuch model with the interference of the outer noise, where there are finite n agents and the evolution is discrete-time. The opinion interaction occurs by one randomly chosen pair at each time step. The difference to the original Deffuant-Weisbuch model is that communications of any selected pairs will be affected by noises. The aim of this paper is to study the robust consensus of this noisy Deffuant-Weisbuch model. We first define the noise strength as the maximum noise absolute value. We will then show that when the noise strength is less than a certain threshold, this noisy model will achieve T-robust consensus when t is sufficiently large; next we prove that the noisy model achieves robust consensus with a positive probability; finally, we demonstrate these results and provide numerical relations among the noise strength and some model parameters.