Fialkowski Jan, Yanchuk Serhiy, Sokolov Igor M, Schöll Eckehard, Gottwald Georg A, Berner Rico
Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany.
Phys Rev Lett. 2023 Feb 10;130(6):067402. doi: 10.1103/PhysRevLett.130.067402.
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, coevolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite-size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multistep transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.
平衡和非平衡系统中的相变在自然科学中起着重要作用。在动态网络中，相变组织了耦合动态单元集体行为的定性变化。自适应动态网络具有随时间变化的连接结构，与节点的动态状态共同演化。在本信函中，我们展示了在有限大小的异质相位振荡器自适应网络中出现的两种不同的一阶非平衡相变。根据内部频率分布中缺陷的性质，我们观察到要么是突然的单步转变为完全同步，要么是更渐进的多步转变。这一观察结果与异质成核有惊人的相似之处。我们开发了一种平均场方法来研究适应性与节点异质性之间的相互作用，并描述多簇状态的动力学及其在确定相变特征中的作用。我们的工作为研究适应性与节点异质性之间的相互作用提供了一个理论框架。
