Jacobo-Villegas Eduardo, Obregón-Quintana Bibiana, Guzmán-Vargas Lev, Liebovitch Larry S
Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico 04510, Mexico.
Unidad Interdisciplinaria en Ingenieria y Tecnologias Avanzadas, Instituto Politecnico Nacional, Av. IPN No. 2580, L. Ticomán, Ciudad de Mexico 07340, Mexico.
Entropy (Basel). 2022 Oct 31;24(11):1571. doi: 10.3390/e24111571.
We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor's state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions leads to a lower separation. Moreover, positive assortative mixing leads to greater divergence between the states, while negative assortative mixing reduces this dispersion. We also find that hierarchical scale-free networks have both similarities and differences when compared with scale-free networks. Hierarchical scale-free networks, like scale-free networks, show the least divergence for an equal mix of cooperative and competitive interactions between actors. On the other hand, hierarchical scale-free networks, unlike scale-free networks, show much greater divergence when dominated by cooperative rather than competitive actors, and while the formation of a rich club (adding links between hubs) with cooperative interactions leads to greater divergence, the divergence is much less when they are fully competitive. Our findings highlight the importance of the topology where the interaction dynamics take place, and the fact that a balanced presence of cooperators and competitors makes the system more cohesive, compared to the case where one strategy dominates.
我们展示了一项关于位于具有无标度和分层无标度拓扑结构且具有同配混合（即参与者度分布之间的相关性）的复杂网络上的参与者之间动态相互作用的研究。参与者的状态根据一个模型演化，该模型考虑其先前状态、变化的惯性以及其邻域的影响。我们表明，系统的时间演化取决于合作或竞争相互作用的百分比。对于无标度网络，我们发现当所有相互作用都是合作性或竞争性时，参与者之间的分散度更高，而相互作用的平衡存在会导致较低的分离度。此外，正同配混合会导致状态之间的差异更大，而负同配混合会减少这种分散度。我们还发现，与无标度网络相比，分层无标度网络既有相似之处也有不同之处。分层无标度网络与无标度网络一样，在参与者之间合作和竞争相互作用均等混合时显示出最小的差异。另一方面，分层无标度网络与无标度网络不同，当由合作而非竞争的参与者主导时，显示出更大的差异，并且虽然具有合作相互作用的富俱乐部（在枢纽之间添加链接）的形成会导致更大的差异，但当它们完全竞争时差异要小得多。我们的研究结果突出了相互作用动态发生的拓扑结构的重要性，以及与一种策略占主导的情况相比，合作者和竞争者的平衡存在使系统更具凝聚力这一事实。
