We systematically study a concealed voter model with heterogeneous reaction rates including the copying rate, externalization rate and internalization rate of each voter, which corresponds to the heterogeneity of activity of real people. By means of heterogeneous mean-field treatment, we derive the evolution equations of the system which allow us to construct a conserved quantity that governs the dynamical process. And furthermore, we also obtain the analytical expressions for the consensus time along with the exit probability. Our studies suggest that the heterogeneous copying rate and internalization rate can decelerate the consensus process, whereas the heterogeneous externalization rate does the opposite but slightly. All the analytical predictions are validated by extensive computer simulations.

中文翻译：

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选民活动异质的隐蔽选民模型中的共识时间

我们系统地研究了一个隐蔽的选民模型，该模型具有异质反应率，包括每个选民的复制率、外化率和内化率，它对应于真实人活动的异质性。通过异质平均场处理，我们推导出系统的演化方程，使我们能够构造一个控制动力学过程的守恒量。此外，我们还获得了共识时间和退出概率的解析表达式。我们的研究表明，异质复制率和内化率可以减慢共识过程，而异质外化率则相反但略有影响。所有的分析预测都经过广泛的计算机模拟验证。