宗教信仰归属动力学模型中的非平衡相变与吸收态
Nonequilibrium phase transitions and absorbing states in a model for the dynamics of religious affiliation
AI总结：
本文提出一个包含三个子群体的宗教信仰归属仓室模型，通过常微分方程与Monte Carlo模拟发现系统存在吸收态、子群体共存区及两个临界点，结果与北爱尔兰数据定性吻合，并探讨了不灵活个体的影响。
摘要：
我们提出了一个简单的模型来描述宗教信仰归属的动力学。为此，我们构建了一个包含三个不同子群体的仓室模型，即虔诚的宗教信徒、不虔诚的宗教信徒和无宗教归属的个体。各仓室之间的转换由概率控制，模拟了群体间的社会互动以及仓室间的自发转换。首先，我们在全连接网络上考虑该模型。因此，我们编写了一组常微分方程来研究子群体的演化。我们的解析和数值结果表明，模型中存在一个吸收态，在长时间极限下只有一个子群体存活。也存在某些参数区域，部分子群体（两个或三个）共存。我们还验证了两个不同临界点的出现。此外，为了分析晶格结构的存在对模型临界行为的影响，我们还提出了模型在二维方格上的 Monte Carlo 模拟。将模型结果与北爱尔兰宗教信仰归属数据进行比较，显示出良好的定性一致性。最后，我们考虑了群体中存在不灵活个体的现象，即从不改变状态的个体。也讨论了此类特殊智能体对模型临界行为的影响。
英文摘要：
We propose a simple model to describe the dynamics of religious affiliation. For such purpose, we built a compartmental model with three distinct subpopulations, namely religious committed individuals, religious noncommitted individuals and not religious affiliated individuals. The transitions among the compartments are governed by probabilities, modeling social interactions among the groups and also spontaneous transitions among the compartments. First of all, we consider the model on a fully-connected network. Thus, we write a set of ordinary differential equations to study the evolution of the subpopulations. Our analytical and numerical results show that there is an absorbing state in the model where only one of the subpopulations survive in the long-time limit. There are also regions of parameters where some of the subpopulations coexist (two or three). We also verified the occurrence of two distinct critical points. In addition, we also present Monte Carlo simulations of the model on two-dimensional square lattices, in order to analyze the impact of the presence of a lattice structure on the critical behavior of the model. Comparison of the models' results with data for religious affiliation in Northern Ireland shows a good qualitative agreement. Finally, we considered the presence of inflexible individuals in the population, i.e., individuals that never change their states. The impact of such special agents on the critical behavior of the model is also discussed.
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