Nirmala Jenifer S, Ghosh Dibakar, Muruganandam Paulsamy
Department of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu, India.
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
Chaos. 2024 Dec 1;34(12). doi: 10.1063/5.0226199.
Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and competitive) commonly observed in systems such as the human brain and social networks. This work addresses this gap by incorporating these factors into a model that explores their impact on collective properties such as synchronization. Through simplified network representations, we investigate how the simultaneous presence of cooperative and competitive adaptations influences phase transitions. Our findings reveal a transition from first-order to second-order synchronization as the strength of higher-order interactions increases under competitive adaptation. We also demonstrate the possibility of synchronization even without pairwise interactions, provided there is strong enough higher-order coupling. When only competitive adaptations are present, the system exhibits second-order-like phase transitions and clustering. Conversely, with a combination of cooperative and competitive adaptations, the system undergoes a first-order-like phase transition, characterized by a sharp transition to the synchronized state without reverting to an incoherent state during backward transitions. The specific nature of these second-order-like transitions varies depending on the coupling strengths and mean degrees. With our model, we can control not only when the system synchronizes but also the way the system goes to synchronization.
自适应网络是描述不同现实世界现象的一种强大表示方式。然而，当前的模型常常忽略高阶相互作用（超出成对相互作用）以及在诸如人类大脑和社会网络等系统中常见的多种适应类型（合作性和竞争性）。这项工作通过将这些因素纳入一个模型来解决这一差距，该模型探索它们对诸如同步等集体属性的影响。通过简化的网络表示，我们研究合作性和竞争性适应的同时存在如何影响相变。我们的研究结果表明，在竞争性适应下，随着高阶相互作用强度的增加，会从一阶同步转变为二阶同步。我们还证明，即使没有成对相互作用，只要存在足够强的高阶耦合，同步也是可能的。当仅存在竞争性适应时，系统呈现出类似二阶的相变和聚类。相反，当合作性和竞争性适应相结合时，系统会经历类似一阶的相变，其特征是急剧转变为同步状态，在反向转变过程中不会恢复到非相干状态。这些类似二阶转变的具体性质取决于耦合强度和平均度。利用我们的模型，我们不仅可以控制系统何时同步，还可以控制系统达到同步的方式。
