带乘性噪声的Agent意见动力学模型中的反馈环
Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise
摘要：
我们引入了一个基于代理的模型，共同发展的意见和社会动态，乘性噪声的影响下。在这个模型中，每个代理的特点是在社会空间中的位置和一个连续的意见状态变量。智能体的运动受其他智能体的位置和意见的影响，同样，意见动态受智能体的空间接近度和他们的意见相似性的影响。使用数值模拟和形式分析，我们研究了意见动态和流动性的代理人在社会空间之间的反馈回路。我们调查的行为，这反弹道导弹在不同的制度，并探讨各种因素的影响，出现的现象，如群体的形成和意见的共识。我们研究了经验分布，并在无限数量的代理人的限制，我们得到了相应的降阶模型由偏微分方程（PDE）。最后，使用数值例子，我们表明，由此产生的偏微分方程模型是一个很好的近似原ABM。
英文摘要：
We introduce an agent-based model for co-evolving opinion and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents' movements are governed by positions and opinions of other agents and similarly, the opinion dynamics is influenced by agents' spatial proximity and their opinion similarity. Using numerical simulations and formal analysis, we study this feedback loop between opinion dynamics and mobility of agents in a social space. We investigate the behavior of this ABM in different regimes and explore the influence of various factors on appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution and in the limit of infinite number of agents we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples we show that a resulting PDE model is a good approximation of the original ABM.
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