Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain.
Phys Rev E. 2019 Aug;100(2-1):022304. doi: 10.1103/PhysRevE.100.022304.
We study a variant of the voter model with multiple opinions; individuals can imitate each other and also change their opinion randomly in mutation events. We focus on the case of a population with all-to-all interaction. A noise-driven transition between regimes with multimodal and unimodal stationary distributions is observed. In the former, the population is mostly in consensus states; in the latter, opinions are mixed. We derive an effective death-birth process, describing the dynamics from the perspective of one of the opinions and use it to analytically compute marginals of the stationary distribution. These calculations are exact for models with homogeneous imitation and mutation rates and an approximation if rates are heterogeneous. Our approach can be used to characterize the noise-driven transition and to obtain mean switching times between consensus states.
我们研究了具有多种观点的投票者模型的变体；个体可以相互模仿，也可以在突变事件中随机改变自己的观点。我们关注的是具有全相互作用的群体的情况。观察到了一种由多峰和单峰平稳分布之间的噪声驱动的转变。在前一种情况下，群体大多处于共识状态；在后一种情况下，观点是混合的。我们推导了一个有效的生死过程，从一个观点的角度描述动力学，并使用它来分析计算平稳分布的边缘。这些计算对于同态模仿和突变率的模型是精确的，如果速率是异构的，则是近似的。我们的方法可以用来描述噪声驱动的转变，并获得共识状态之间的平均切换时间。
