Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland.
IFISC, Institute for Cross-disciplinary Physics and Complex Systems (UIB-CSIC), Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spain.
Sci Rep. 2020 Sep 24;10(1):15660. doi: 10.1038/s41598-020-72662-8.
We study the joint effect of the non-linearity of interactions and noise on coevolutionary dynamics. We choose the coevolving voter model as a prototype framework for this problem. By numerical simulations and analytical approximations we find three main phases that differ in the absolute magnetisation and the size of the largest component: a consensus phase, a coexistence phase, and a dynamical fragmentation phase. More detailed analysis reveals inner differences in these phases, allowing us to divide two of them further. In the consensus phase we can distinguish between a weak or alternating consensus and a strong consensus, in which the system remains in the same state for the whole realisation of the stochastic dynamics. In the coexistence phase we distinguish a fully-mixing phase and a structured coexistence phase, where the number of active links drops significantly due to the formation of two homogeneous communities. Our numerical observations are supported by an analytical description using a pair approximation approach and an ad-hoc calculation for the transition between the coexistence and dynamical fragmentation phases. Our work shows how simple interaction rules including the joint effect of non-linearity, noise, and coevolution lead to complex structures relevant in the description of social systems.
我们研究了相互作用的非线性和噪声对协同进化动力学的联合影响。我们选择共同进化的投票模型作为这个问题的原型框架。通过数值模拟和分析近似，我们发现了三个主要的相位，它们在绝对磁化强度和最大分量的大小上有所不同：共识相位、共存相位和动态分裂相位。更详细的分析揭示了这些相位的内在差异，使我们能够进一步将其中两个相位进一步划分。在共识相位中，我们可以区分弱或交替共识和强共识，在强共识中，系统在随机动力学的整个实现过程中保持相同的状态。在共存相位中，我们区分了完全混合相和结构共存相，其中由于两个均匀社区的形成，活动链接的数量显著下降。我们的数值观察得到了使用配对近似方法和特定于共存和动态分裂相之间的过渡的计算的分析描述的支持。我们的工作表明，包括非线性、噪声和共同进化的联合影响在内的简单相互作用规则如何导致在描述社会系统时相关的复杂结构。
